Organizing Committee
 Jesús De Loera
University of California, Davis  Antoine Deza
McMaster University  Marcia Fampa
Federal University of Rio de Janeiro  Volker Kaibel
OttovonGuericke Universität Magdeburg  Jon Lee
University of Michigan  Laura Sanità
Bocconi University of Milan
Abstract
Discrete optimization is a vibrant area of computational mathematics devoted to efficiently finding optimal solutions among a finite or countable set of possible feasible solutions.
A famous and classical example of a problem in discrete optimization is the traveling salesperson problem: For given cities and distances of traveling from one city to another, we seek to find the shortest route that visits each city once and returns to the starting city. Discrete optimization problems naturally arise in many kinds of applications including bioinformatics, telecommunications network design, airline scheduling, circuit design, and efficient resource allocation. The field also connects to a variety of areas in mathematics, computer science, and data analytics including approximation algorithms, convex and tropical geometry, number theory, real algebraic geometry, parameterized complexity theory, quantum computing, machine learning, and mathematical logic.
The semester program will explore links between mathematical tools and unsolved fundamental questions in these areas. We plan to explore computational techniques from discrete optimization to experimentally attack classical problems in combinatorics and other areas of pure mathematics. We will also continue the tradition of designing new algorithms for applied and industrial problems which has been part of the subject since its inception. By bringing together a diverse group of researchers, we anticipate making new connections and collaborations as well as deepening existing ones.
Confirmed Speakers & Participants
Talks will be presented virtually or inperson as indicated in the schedule below.
 Speaker
 Poster Presenter
 Attendee
 Virtual Attendee

Ahmad Abdi
London School of EconomicsMar 26Apr 8, 2023

Tobias Achterberg
Gurobi OptimizationApr 2428, 2023

Hessa AlThani
University of MichiganJan 29May 5, 2023

Rachael Alfant
Rice UniversityApr 2428, 2023

Carlos Alfaro Montufar
Banco de MexicoMar 26Apr 1, 2023

Félix Almendra Hernández
UC DavisJan 30Feb 3, 2023

Miguel Anjos
University of EdinburghFeb 27Mar 3, 2023; Mar 17Apr 7, 2023

Kurt Anstreicher
University of IowaFeb 26Apr 28, 2023

Nicholas Arosemena
Brown UniversityJan 30Feb 3, 2023

Nancy Maribel Arratia Martinez
Universidad de las Américas PueblaJan 29May 6, 2023

Alper Atamturk
University of California  BerkeleyFeb 27Mar 3, 2023

Gennady Averkov
Brandeburg Technical UniversityFeb 27Mar 3, 2023

Utsav Awasthi
University of ConnecticutFeb 27Mar 3, 2023

Catherine Babecki
University of Washington, SeattleFeb 23May 5, 2023

Suman Balasubramanian
DePauw UniversityMar 2631, 2023

Ishan Bansal
Cornell UniversityJan 30Feb 3, 2023

Amitabh Basu
Johns Hopkins UniversityApr 2May 6, 2023

Pietro Belotti
Politecnico di MilanoFeb 26Mar 10, 2023; Apr 2329, 2023

Hande Benson
Drexel UniversityFeb 27Mar 3, 2023

Daniel Bienstock
Columbia UniversityFeb 27Mar 3, 2023

Alex Black
UC DavisJan 30May 5, 2023

Merve Bodur
University of TorontoFeb 27Mar 3, 2023

Tristram Bogart
Universidad de los AndesMar 2631, 2023

Steffen Borgwardt
University of Colorado DenverMar 2731, 2023

Enrico Bortoletto
Zuse Institute BerlinMar 2731, 2023

MarieCharlotte Brandenburg
Max Planck Institute for Mathematics in the SciencesMar 26Apr 8, 2023

Hauke Brinkop
Kiel UniversityFeb 26Mar 3, 2023

DENISE CARIAGA SANDOVAL
University of EdinburghFeb 26Mar 3, 2023

Martina Cerulli
ESSEC Business School of ParisFeb 26Mar 4, 2023

Teressa Chambers
Brown UniversityJan 30Feb 3, 2023; Mar 2731, 2023; Apr 2428, 2023

Karthekeyan Chandrasekaran
University of Illinois UrbanaChampaignFeb 6May 6, 2023

Effrosyni Chasioti
Kent State UniversityJan 30May 6, 2023

Zhongzhu Chen
University of MichiganJan 30Apr 2, 2023

Lin Chen
Texas Tech UniversityFeb 27Mar 3, 2023

Carleton Coffrin
Los Alamos National LaboratoryApr 2428, 2023

Vincent CohenAddad
CNRS & Sorbonne UniversitéMar 2731, 2023

Andrei Comăneci
Technische Universität BerlinMar 2731, 2023

Gerard Cornuejols
Carnegie Mellon UniversityMar 19Apr 7, 2023

Ryan CoryWright
IBM Research and Imperial College LondonFeb 27Mar 3, 2023

Francisco Criado Gallart
CUNEF UniversidadJan 30Apr 29, 2023

Claudia D'Ambrosio
LIX  Ecole PolytechniqueMar 26May 6, 2023

Daniel Dadush
Centrum Wiskunde & InformaticaMar 26Apr 29, 2023

Maria Dascalu
University of Massachusetts AmherstJan 29Feb 4, 2023

Sanjeeb Dash
IBM ResearchMar 2731, 2023

Jesús De Loera
University of California, DavisJan 29May 6, 2023

Daniel de Roux
Carnegie Mellon UniversityFeb 26Mar 5, 2023; Apr 2328, 2023

Alberto Del Pia
University of WisconsinMadisonFeb 26Mar 4, 2023

Santanu Dey
Georgia Institute of Technology.Apr 1030, 2023

Antoine Deza
McMaster UniversityMar 26Apr 22, 2023

Bistra Dilkina
University of Southern CaliforniaApr 28, 2023

Alina Ene
Boston UniversityMar 2731, 2023

Daniel Espinoza
Google ResearchFeb 26Mar 4, 2023

Yuri Faenza
Columbia UniversityJan 29Feb 2, 2023; Feb 68, 2023; Feb 1415, 2023; Feb 2728, 2023; Mar 910, 2023; Mar 1519, 2023; Mar 2324, 2023; Mar 2728, 2023; Apr 1314, 2023; Apr 1718, 2023; Apr 2425, 2023; May 12, 2023

Marcia Fampa
Federal University of Rio de JaneiroJan 29May 6, 2023

Samuel Fiorini
Université libre de BruxellesMar 26Apr 1, 2023

Allison Fitisone
University of KentuckyJan 30Feb 3, 2023; Mar 2731, 2023; Apr 2428, 2023

Antonio Frangioni
Università di PisaFeb 27Mar 3, 2023

Ricardo Fukasawa
University of WaterlooFeb 27Mar 3, 2023; Apr 2428, 2023

Raul Garcia
Rice UniversityApr 2428, 2023

Rohan Ghuge
University of MichiganJan 30Apr 3, 2023

Ambros Gleixner
HTW & Zuse Institute BerlinApr 2329, 2023

Michel Goemans
Massachusetts Institute of TechnologyMar 2831, 2023

Andres Gomez
University of Southern CaliforniaFeb 26Mar 4, 2023

Weston Grewe
University of Colorado DenverJan 30Feb 3, 2023

Monserrat Guedes Ayala
The University of EdinburghFeb 27Mar 3, 2023

Oktay Gunluk
Cornell UniversityFeb 26Mar 4, 2023

Swati Gupta
Georgia TechMar 26Apr 1, 2023; Apr 2329, 2023

Anupam Gupta
Carnegie Mellon UniversityMar 2731, 2023

Akshay Gupte
University of EdinburghFeb 27Mar 3, 2023

Chengyue He
Columbia UniversityJan 29May 6, 2023

Christoph Hertrich
The London School of Economics and Political ScienceMar 25May 6, 2023

Illya Hicks
Rice UniversityMar 26Apr 1, 2023

Dorit Hochbaum
University of California, BerkeleyFeb 27Mar 3, 2023

Fred Holt
TMobileFeb 27Mar 3, 2023

Joey Huchette
GoogleApr 2329, 2023

Sophie Huiberts
Columbia UniversityMar 26Apr 1, 2023

Dylan HyattDenesik
Eindhoven University of TechnologyJan 28Feb 5, 2023

Satoru Iwata
University of TokyoMar 2731, 2023

Olaniyi Iyiola
Clarkson UniversityMar 26Apr 1, 2023

Klaus Jansen
Kiel UniversityFeb 26Mar 8, 2023; Mar 2731, 2023

Stefanie Jegelka
MITApr 2428, 2023

Sean Kafer
University of WaterlooJan 29May 7, 2023

Volker Kaibel
OttovonGuericke Universität MagdeburgApr 2029, 2023

Lennart Kauther
RWTH Aachen UniversityJan 29Feb 4, 2023; Mar 26Apr 1, 2023

Aleksandr Kazachkov
University of FloridaApr 2428, 2023

Aida Khajavirad
Lehigh UniversityJan 30Feb 3, 2023; Feb 27Mar 3, 2023

Sammy Khalife
Johns Hopkins UniversityJan 30May 5, 2023

Fatma KılınçKarzan
Carnegie Mellon UniversityFeb 27Mar 3, 2023

Nathan Klein
University of WashingtonMar 26Apr 1, 2023

Zhuan Khye Koh
Centrum Wiskunde en InformaticaMar 26Apr 15, 2023

Matthias Köppe
UC DavisFeb 27Mar 3, 2023

Simge Küçükyavuz
Northwestern UniversityFeb 26Mar 4, 2023

Shubhang Kulkarni
University of Illinois, UrbanaChampaignJan 29May 6, 2023

Anatoliy Kuznetsov
Georgia Institute of TechnologyFeb 27Mar 3, 2023

Hélène Langlois
ENPCMar 26Apr 1, 2023

Jon Lee
University of MichiganJan 29May 6, 2023

Yoonsang Lee
Dartmouth CollegeMar 2731, 2023

Miguel Lejeune
George Washington UniversityFeb 27Mar 3, 2023

Yongchun Li
Georgia Institute of TechnologyFeb 27Mar 3, 2023

Leo Liberti
Ecole PolytechniqueApr 2428, 2023

Jeff Linderoth
University of WisconsinMadisonFeb 27Mar 3, 2023

Siyue Liu
Carnegie Mellon UniversityFeb 27Mar 3, 2023; Mar 2731, 2023

Feng Liu
Stevens Institute of TechnologyFeb 27Mar 2, 2023

Vasilis Livanos
University of Illinois UrbanaChampaignMar 25Apr 1, 2023

Andrea Lodi
Cornell TechApr 330, 2023

Daniel Loredo Duran
Columbia UniversityApr 2428, 2023

Miles Lubin
Hudson River TradingApr 2329, 2023

Moira MacNeil
University of TorontoMar 2631, 2023

Tobia Marcucci
MITFeb 26Mar 4, 2023

Juan Carlos Martinez Mori
Cornell UniversityJan 29May 5, 2023

Berenike Masing
Zuse Institute BerlinMar 26Apr 1, 2023

Rahul Mazumder
Massachusetts Institute of TechnologyApr 2428, 2023

Catherine McGeoch
DWave Systems Inc.Apr 2428, 2023

Chiara Meroni
ICERMJan 30Jun 2, 2023

Frédéric Meunier
École Nationale des Ponts et Chaussées, CERMICSApr 5May 5, 2023

Jared Miller
Northeastern UniversityJan 30Feb 3, 2023; Mar 27, 2023

Cristina MoleroRío
École PolytechniqueApr 24May 3, 2023

Gonzalo Muñoz
Universidad de O'HigginsFeb 26Mar 4, 2023

Giacomo Nannicini
University of Southern CaliforniaApr 2428, 2023

Anand Natarajan
MITApr 2428, 2023

Bento Natura
Georgia TechJan 29May 6, 2023

Neil Olver
London School of EconomicsMar 2731, 2023

Shmuel Onn
Technion  Israel Institute of TechnologyMar 14May 6, 2023

Yuchong Pan
MITJan 30May 5, 2023

Dimitri Papadimitriou
University of AntwerpFeb 27Mar 3, 2023

Ojas Parekh
Sandia National LaboratoriesApr 2329, 2023

Ethan Partida
BrownJan 30Feb 3, 2023

Kanstantsin Pashkovich
University of WaterlooMar 2731, 2023

Britta Peis
RWTH Aachen UniversityMar 2731, 2023

Marc Pfetsch
TU DarmstadtFeb 27Mar 3, 2023; Apr 2428, 2023

Sebastian Pokutta
Zuse Institute Berlin (ZIB)Mar 2531, 2023

Gabriel Ponte
Federal University of Rio de JaneiroJan 29Feb 10, 2023

Lionel Pournin
University of Paris 13Mar 26Apr 22, 2023

Tianjie Qiu
Brown UniversityJan 30May 5, 2023

Yushan Qu
University of MichiganFeb 27Mar 3, 2023

Rodolfo Quintero Ospina
Lehigh UniversityJan 30Feb 3, 2023; Feb 27Mar 3, 2023; Apr 2428, 2023

Annie Raymond
University of Massachusetts, AmherstMar 26Apr 1, 2023

Eleanor Rieffel
NASAApr 2428, 2023

Bárbara Rodrigues
University of EdinburghFeb 26Mar 4, 2023

Thomas Rothvoss
University of WashingtonMar 26Apr 1, 2023

Michael Roysdon
Tel Aviv UniversitySep 1, 2022May 5, 2023

Nick Sahinidis
Georgia Institute of TechnologyFeb 27Mar 3, 2023; Apr 2329, 2023

Laura Sanità
Bocconi University of MilanJan 29Feb 4, 2023; Mar 2731, 2023

Lisa Sauermann
MITMar 2731, 2023

Nimita Shinde
IITBMonash Research AcademySep 1, 2022May 31, 2023

Mohit Singh
Georgia TechMar 2631, 2023

Martin Skutella
TU BerlinMar 2631, 2023

Masoumeh Soleimani Amirshekari
Wesleyan university/ CRECMar 2731, 2023

Renata Sotirov
Tilburg UniversityFeb 26Mar 4, 2023

Emily Speakman
University of Colorado  DenverFeb 26Mar 4, 2023

Renan Spencer Trindade
École Polytechnique, FranceApr 24May 4, 2023

Reed Spitzer
Brown UniversityApr 2428, 2023

Nagisa Sugishita
University of EdinburghApr 2428, 2023

Shengding Sun
Georgia Institute of TechnologyMar 2731, 2023

Ola Svensson
EPFLMar 26Apr 1, 2023

Mohit Tawarmalani
Purdue UniversityFeb 27Mar 3, 2023

Christian Tjandraatmadja
GoogleApr 2428, 2023

Vera Traub
University of BonnJan 29Feb 4, 2023

Madison Van Dyk
University of WaterlooApr 2329, 2023

László Végh
London School of EconomicsMar 26Apr 8, 2023

Mauricio Velasco
Universidad de Los AndesJan 29Feb 4, 2023

Lucy Verberk
Eindhoven University of TechnologyJan 29Feb 3, 2023

Juan Pablo Vielma
GoogleApr 2329, 2023

Aapeli Vuorinen
Columbia UniversityJan 30Feb 3, 2023

Jens Vygen
University of BonnMar 2731, 2023

Fei Wang
University of WaterlooJan 31Mar 1, 2023

Jie Wang
Georgia Institute of TechnologyFeb 27Mar 3, 2023

Chengyang Wang
UC DavisJan 30Feb 3, 2023; Feb 27Mar 3, 2023

Stefan Weltge
Technical University of MunichMar 24Apr 1, 2023

William Wesley
University of California DavisJan 30Feb 3, 2023; Apr 2428, 2023

Weijun Xie
Georgia Institute of TechnologyFeb 27Mar 3, 2023

Luze Xu
University of California, DavisJan 29Apr 2, 2023

Chao Xu
University of Electronic Science and Technology of ChinaJan 30Feb 3, 2023; Feb 27Mar 3, 2023; Mar 2731, 2023

Liding Xu
ECOLE POLYTECHNIQUEFeb 27Mar 3, 2023; Mar 2731, 2023; Apr 2428, 2023

Youngho Yoo
Texas A&M UniversityMar 2731, 2023

Rico Zenklusen
ETH ZurichMar 26Apr 1, 2023

Shixuan Zhang
Brown UniversitySep 6, 2022May 5, 2023

Yuan Zhou
University of KentuckyJan 29May 6, 2023

Hang Zhou
Ecole PolytechniqueMar 26Apr 1, 2023

Yiran Zhu
The University of EdinburghFeb 27Mar 3, 2023; Apr 2428, 2023

Michael Zlatin
Carnegie Mellon UniversityMar 2731, 2023
Visit dates listed on the participant list may be tentative and subject to change without notice.
Semester Schedule
Monday, January 30, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

8:30  9:30 am ESTCheck In11th Floor Collaborative Space

9:30  9:50 am ESTCheck In11th Floor Collaborative Space

9:50  10:00 am ESTWelcome11th Floor Lecture Hall
 Brendan Hassett, ICERM/Brown University

10:00  11:00 am ESTMatching Theory and School ChoiceSeminar  11th Floor Lecture Hall
 Speaker
 Yuri Faenza, Columbia University
 Session Chair
 Jon Lee, University of Michigan
Abstract
Many questions in resource allocation can be formulated as matching problems, where nodes represent the agents/goods, and each node corresponding to an agent is endowed with a preference profile on the (sets of) its neighbors in the graph. Starting with the classical marriage setting by Gale and Shapley, we will investigate algorithmic and structural properties of these models, and discuss applications to the problem of allocating seats in public schools.

11:00  11:30 am ESTCoffee Break11th Floor Collaborative Space

11:30 am  12:30 pm ESTMatching Theory and School ChoiceSeminar  11th Floor Lecture Hall
 Speaker
 Yuri Faenza, Columbia University
 Session Chair
 Jon Lee, University of Michigan
Abstract
Many questions in resource allocation can be formulated as matching problems, where nodes represent the agents/goods, and each node corresponding to an agent is endowed with a preference profile on the (sets of) its neighbors in the graph. Starting with the classical marriage setting by Gale and Shapley, we will investigate algorithmic and structural properties of these models, and discuss applications to the problem of allocating seats in public schools.

12:30  2:30 pm ESTLunch/Free Time

2:30  3:30 pm ESTBinary polynomial optimization: theory, algorithms, and applicationsSeminar  11th Floor Lecture Hall
 Speaker
 Aida Khajavirad, Lehigh University
 Session Chair
 Marcia Fampa, Federal University of Rio de Janeiro
Abstract
In this minicourse, I present an overview of some recent advances in the theory of binary polynomial optimization together with specific applications in data science and machine learning. First utilizing a hypergraph representation scheme, I describe the connection between hypergraph acyclicity and the complexity of unconstrained binary polynomial optimization. As a byproduct, I present strong linear programming relaxations for general binary polynomial optimization problems and demonstrate their impact via extensive numerical experiments. Finally, I focus on two applications from data science, namely, Boolean tensor factorization and higherorder Markov random fields, and demonstrate how our theoretical findings enable us to obtain efficient algorithms with theoretical performance guarantees for these applications.

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space

4:00  5:00 pm ESTBinary polynomial optimization: theory, algorithms, and applicationsSeminar  11th Floor Lecture Hall
 Speaker
 Aida Khajavirad, Lehigh University
 Session Chair
 Marcia Fampa, Federal University of Rio de Janeiro
Abstract
In this minicourse, I present an overview of some recent advances in the theory of binary polynomial optimization together with specific applications in data science and machine learning. First utilizing a hypergraph representation scheme, I describe the connection between hypergraph acyclicity and the complexity of unconstrained binary polynomial optimization. As a byproduct, I present strong linear programming relaxations for general binary polynomial optimization problems and demonstrate their impact via extensive numerical experiments. Finally, I focus on two applications from data science, namely, Boolean tensor factorization and higherorder Markov random fields, and demonstrate how our theoretical findings enable us to obtain efficient algorithms with theoretical performance guarantees for these applications.

5:00  6:30 pm ESTReception11th Floor Collaborative Space
Tuesday, January 31, 2023

9:00  10:00 am ESTApproximation Algorithms for Network Design ProblemsSeminar  11th Floor Lecture Hall
 Speaker
 Vera Traub, University of Bonn
 Session Chair
 Laura Sanità, Bocconi University of Milan
Abstract
The goal of network design is to construct cheap networks that satisfy certain connectivity requirements. A celebrated result by Jain [Combinatorica, 2001] provides a 2approximation algorithm for a wide class of these problems. However, even for many very basic special cases nothing better is known. In this lecture series, we present an introduction and some of the new techniques underlying recent advances in this area. These techniques led for example to a new algorithm for the Steiner Tree Problem and to the first betterthan2 approximation algorithm for Weighted Connectivity Augmentation.

10:00  10:30 am ESTCoffee Break11th Floor Collaborative Space

10:30  11:30 am ESTApproximation Algorithms for Network Design ProblemsSeminar  11th Floor Lecture Hall
 Speaker
 Vera Traub, University of Bonn
 Session Chair
 Laura Sanità, Bocconi University of Milan
Abstract
The goal of network design is to construct cheap networks that satisfy certain connectivity requirements. A celebrated result by Jain [Combinatorica, 2001] provides a 2approximation algorithm for a wide class of these problems. However, even for many very basic special cases nothing better is known. In this lecture series, we present an introduction and some of the new techniques underlying recent advances in this area. These techniques led for example to a new algorithm for the Steiner Tree Problem and to the first betterthan2 approximation algorithm for Weighted Connectivity Augmentation.

11:45 am  1:00 pm ESTProblem Session11th Floor Lecture Hall

1:00  3:00 pm ESTLunch/Free Time

3:00  5:00 pm EST
Wednesday, February 1, 2023

9:00  10:00 am ESTPolynomial optimization on finite setsSeminar  11th Floor Lecture Hall
 Speaker
 Mauricio Velasco, Universidad de Los Andes
 Session Chair
 Jesús De Loera, University of California, Davis
Abstract
If $X\subseteq \mathbb{R}^n$ is a finite set then every function on $X$ can be written as the restriction of a polynomial in nvariables. As a result, polynomial optimization on finite sets is literally the same as general (nonlinear) optimization on such sets. Thinking of functions as polynomials, however, provides us with plenty of additional structures which can be leveraged for constructing better (or at least different) optimization algorithms. In these lectures, we will overview some of the key problems and results coming from this algebraic point of view. Specifically, we will discuss: How to prove that a polynomial function is nonnegative on a finite set X? What kind of algebraic certificates (proofs) are available and what can we say about their size and complexity? If the set $X$ has symmetries, can we leverage them in some systematic way that is useful for optimization? Characterizing the affine linear functions that are nonnegative on $X$ gives a description of the polytope $P={\rm Conv}(X)$. Stratifying such functions by the degree of their nonnegativity certificates leads to (semidefinite) hierarchies of approximation for the polytope $P$ and it is natural to ask about their speed of convergence and its relationship with the combinatorics of $P$ Finally, if time permits we will discuss some recent ideas combining the above methods with reinforcement learning as a way to improve scalability for combinatorial optimization problems. The results in (1),(2), (3) above are due to Blekherman, Gouveia, Laurent, Nie, Parrilo, Saunderson, Thomas, and others. These lectures intend to be a selfcontained introduction to this vibrant and exciting research area.

10:00  10:30 am ESTCoffee Break11th Floor Collaborative Space

10:30  11:30 am ESTPolynomial optimization on finite setsSeminar  11th Floor Lecture Hall
 Speaker
 Mauricio Velasco, Universidad de Los Andes
 Session Chair
 Jesús De Loera, University of California, Davis
Abstract
If $X\subseteq \mathbb{R}^n$ is a finite set then every function on $X$ can be written as the restriction of a polynomial in nvariables. As a result, polynomial optimization on finite sets is literally the same as general (nonlinear) optimization on such sets. Thinking of functions as polynomials, however, provides us with plenty of additional structures which can be leveraged for constructing better (or at least different) optimization algorithms. In these lectures, we will overview some of the key problems and results coming from this algebraic point of view. Specifically, we will discuss: How to prove that a polynomial function is nonnegative on a finite set X? What kind of algebraic certificates (proofs) are available and what can we say about their size and complexity? If the set $X$ has symmetries, can we leverage them in some systematic way that is useful for optimization? Characterizing the affine linear functions that are nonnegative on $X$ gives a description of the polytope $P={\rm Conv}(X)$. Stratifying such functions by the degree of their nonnegativity certificates leads to (semidefinite) hierarchies of approximation for the polytope $P$ and it is natural to ask about their speed of convergence and its relationship with the combinatorics of $P$ Finally, if time permits we will discuss some recent ideas combining the above methods with reinforcement learning as a way to improve scalability for combinatorial optimization problems. The results in (1),(2), (3) above are due to Blekherman, Gouveia, Laurent, Nie, Parrilo, Saunderson, Thomas, and others. These lectures intend to be a selfcontained introduction to this vibrant and exciting research area.

11:40  11:45 am ESTGroup Photo (Immediately After Talk)11th Floor Lecture Hall

11:45 am  2:00 pm ESTLunch/Free Time

2:00  3:00 pm ESTMatching Theory and School ChoiceSeminar  11th Floor Lecture Hall
 Speaker
 Yuri Faenza, Columbia University
 Session Chair
 Jon Lee, University of Michigan
Abstract
Many questions in resource allocation can be formulated as matching problems, where nodes represent the agents/goods, and each node corresponding to an agent is endowed with a preference profile on the (sets of) its neighbors in the graph. Starting with the classical marriage setting by Gale and Shapley, we will investigate algorithmic and structural properties of these models, and discuss applications to the problem of allocating seats in public schools.

3:00  3:30 pm ESTCoffee Break11th Floor Collaborative Space

3:30  4:30 pm ESTMatching Theory and School ChoiceSeminar  11th Floor Lecture Hall
 Speaker
 Yuri Faenza, Columbia University
 Session Chair
 Jon Lee, University of Michigan
Abstract
Many questions in resource allocation can be formulated as matching problems, where nodes represent the agents/goods, and each node corresponding to an agent is endowed with a preference profile on the (sets of) its neighbors in the graph. Starting with the classical marriage setting by Gale and Shapley, we will investigate algorithmic and structural properties of these models, and discuss applications to the problem of allocating seats in public schools.
Thursday, February 2, 2023

9:00  10:00 am ESTApproximation Algorithms for Network Design ProblemsSeminar  11th Floor Lecture Hall
 Speaker
 Vera Traub, University of Bonn
 Session Chair
 Laura Sanità, Bocconi University of Milan
Abstract
The goal of network design is to construct cheap networks that satisfy certain connectivity requirements. A celebrated result by Jain [Combinatorica, 2001] provides a 2approximation algorithm for a wide class of these problems. However, even for many very basic special cases nothing better is known. In this lecture series, we present an introduction and some of the new techniques underlying recent advances in this area. These techniques led for example to a new algorithm for the Steiner Tree Problem and to the first betterthan2 approximation algorithm for Weighted Connectivity Augmentation.

10:00  10:30 am ESTCoffee Break11th Floor Collaborative Space

10:30  11:30 am ESTApproximation Algorithms for Network Design ProblemsSeminar  11th Floor Lecture Hall
 Speaker
 Vera Traub, University of Bonn
 Session Chair
 Laura Sanità, Bocconi University of Milan
Abstract
The goal of network design is to construct cheap networks that satisfy certain connectivity requirements. A celebrated result by Jain [Combinatorica, 2001] provides a 2approximation algorithm for a wide class of these problems. However, even for many very basic special cases nothing better is known. In this lecture series, we present an introduction and some of the new techniques underlying recent advances in this area. These techniques led for example to a new algorithm for the Steiner Tree Problem and to the first betterthan2 approximation algorithm for Weighted Connectivity Augmentation.

11:30 am  1:30 pm ESTLunch/Free Time

1:30  2:30 pm ESTBinary polynomial optimization: theory, algorithms, and applicationsSeminar  11th Floor Lecture Hall
 Speaker
 Aida Khajavirad, Lehigh University
 Session Chair
 Marcia Fampa, Federal University of Rio de Janeiro
Abstract
In this minicourse, I present an overview of some recent advances in the theory of binary polynomial optimization together with specific applications in data science and machine learning. First utilizing a hypergraph representation scheme, I describe the connection between hypergraph acyclicity and the complexity of unconstrained binary polynomial optimization. As a byproduct, I present strong linear programming relaxations for general binary polynomial optimization problems and demonstrate their impact via extensive numerical experiments. Finally, I focus on two applications from data science, namely, Boolean tensor factorization and higherorder Markov random fields, and demonstrate how our theoretical findings enable us to obtain efficient algorithms with theoretical performance guarantees for these applications.

2:30  3:30 pm ESTCoffee Break11th Floor Collaborative Space

3:30  4:30 pm ESTRankone Boolean tensor factorization and the multilinear polytopeSeminar  11th Floor Lecture Hall
 Speaker
 Aida Khajavirad, Lehigh University
 Session Chair
 Marcia Fampa, Federal University of Rio de Janeiro
Abstract
In this minicourse, I present an overview of some recent advances in the theory of binary polynomial optimization together with specific applications in data science and machine learning. First utilizing a hypergraph representation scheme, I describe the connection between hypergraph acyclicity and the complexity of unconstrained binary polynomial optimization. As a byproduct, I present strong linear programming relaxations for general binary polynomial optimization problems and demonstrate their impact via extensive numerical experiments. Finally, I focus on two applications from data science, namely, Boolean tensor factorization and higherorder Markov random fields, and demonstrate how our theoretical findings enable us to obtain efficient algorithms with theoretical performance guarantees for these applications.
Friday, February 3, 2023

10:00  11:00 am ESTPolynomial optimization on finite setsSeminar  11th Floor Lecture Hall
 Speaker
 Mauricio Velasco, Universidad de Los Andes
 Session Chair
 Jesús De Loera, University of California, Davis
Abstract
If $X\subseteq \mathbb{R}^n$ is a finite set then every function on $X$ can be written as the restriction of a polynomial in nvariables. As a result, polynomial optimization on finite sets is literally the same as general (nonlinear) optimization on such sets. Thinking of functions as polynomials, however, provides us with plenty of additional structures which can be leveraged for constructing better (or at least different) optimization algorithms. In these lectures, we will overview some of the key problems and results coming from this algebraic point of view. Specifically, we will discuss: How to prove that a polynomial function is nonnegative on a finite set X? What kind of algebraic certificates (proofs) are available and what can we say about their size and complexity? If the set $X$ has symmetries, can we leverage them in some systematic way that is useful for optimization? Characterizing the affine linear functions that are nonnegative on $X$ gives a description of the polytope $P={\rm Conv}(X)$. Stratifying such functions by the degree of their nonnegativity certificates leads to (semidefinite) hierarchies of approximation for the polytope $P$ and it is natural to ask about their speed of convergence and its relationship with the combinatorics of $P$ Finally, if time permits we will discuss some recent ideas combining the above methods with reinforcement learning as a way to improve scalability for combinatorial optimization problems. The results in (1),(2), (3) above are due to Blekherman, Gouveia, Laurent, Nie, Parrilo, Saunderson, Thomas, and others. These lectures intend to be a selfcontained introduction to this vibrant and exciting research area.

11:00  11:30 am ESTCoffee Break11th Floor Collaborative Space

11:30 am  12:30 pm ESTPolynomial optimization on finite setsSeminar  11th Floor Lecture Hall
 Speaker
 Mauricio Velasco, Universidad de Los Andes
 Session Chair
 Jesús De Loera, University of California, Davis
Abstract
If $X\subseteq \mathbb{R}^n$ is a finite set then every function on $X$ can be written as the restriction of a polynomial in nvariables. As a result, polynomial optimization on finite sets is literally the same as general (nonlinear) optimization on such sets. Thinking of functions as polynomials, however, provides us with plenty of additional structures which can be leveraged for constructing better (or at least different) optimization algorithms. In these lectures, we will overview some of the key problems and results coming from this algebraic point of view. Specifically, we will discuss: How to prove that a polynomial function is nonnegative on a finite set X? What kind of algebraic certificates (proofs) are available and what can we say about their size and complexity? If the set $X$ has symmetries, can we leverage them in some systematic way that is useful for optimization? Characterizing the affine linear functions that are nonnegative on $X$ gives a description of the polytope $P={\rm Conv}(X)$. Stratifying such functions by the degree of their nonnegativity certificates leads to (semidefinite) hierarchies of approximation for the polytope $P$ and it is natural to ask about their speed of convergence and its relationship with the combinatorics of $P$ Finally, if time permits we will discuss some recent ideas combining the above methods with reinforcement learning as a way to improve scalability for combinatorial optimization problems. The results in (1),(2), (3) above are due to Blekherman, Gouveia, Laurent, Nie, Parrilo, Saunderson, Thomas, and others. These lectures intend to be a selfcontained introduction to this vibrant and exciting research area.

12:30  2:30 pm ESTLunch/Free Time

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Monday, February 6, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

9:30  10:00 am ESTICERM Director and Organizer WelcomeWelcome  11th Floor Lecture Hall
 Jesús De Loera, University of California, Davis
 Marcia Fampa, Federal University of Rio de Janeiro
 Brendan Hassett, ICERM/Brown University
 Volker Kaibel, OttovonGuericke Universität Magdeburg
 Jon Lee, University of Michigan

3:30  4:30 pm ESTInformal TeaCoffee Break  11th Floor Collaborative Space
Tuesday, February 7, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

9:30  10:30 am ESTDirector/Organizer MeetingMeeting  11th Floor Conference Room

12:00  1:00 pm ESTPostdoc/Graduate Student Meeting with ICERM DirectorMeeting  11th Floor Lecture Hall

2:30  3:30 pm ESTMeet to organize the mother of all seminar(s)Meeting  11th Floor Lecture Hall

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Wednesday, February 8, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

10:00  10:05 am ESTHessa AlThani IntroductionLightning Talks  11th Floor Lecture Hall

10:05  10:10 am ESTAlex Black IntroductionLightning Talks  11th Floor Lecture Hall

10:10  10:15 am ESTZhongzhu Chen IntroductionLightning Talks  11th Floor Lecture Hall

10:15  10:20 am ESTRohan Ghuge IntroductionLightning Talks  11th Floor Lecture Hall

10:20  10:25 am ESTChengyue He IntroductionLightning Talks  11th Floor Lecture Hall

10:25  10:30 am ESTJuan Carlos Martinez Mori IntroductionLightning Talks  11th Floor Lecture Hall

10:30  10:40 am ESTSean Kafer IntroductionLightning Talks  11th Floor Lecture Hall

10:40  10:50 am ESTSammy Khalife IntroductionLightning Talks  11th Floor Lecture Hall

10:50  11:00 am ESTChiara Meroni IntroductionLightning Talks  11th Floor Lecture Hall

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Thursday, February 9, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

10:00  10:05 am ESTGabriel Ponte IntroductionLightning Talks  11th Floor Lecture Hall

10:05  10:10 am ESTTianjie Qiu IntroductionLightning Talks  11th Floor Lecture Hall

10:15  10:25 am ESTBento Natura IntroductionLightning Talks  11th Floor Lecture Hall

10:25  10:35 am ESTMichael Roysdon IntroductionLightning Talks  11th Floor Lecture Hall

10:35  10:45 am ESTNimita Shinde IntroductionLightning Talks  11th Floor Lecture Hall

10:45  10:55 am ESTFei Wang IntroductionLightning Talks  11th Floor Lecture Hall

10:55  11:05 am ESTLuze Xu IntroductionLightning Talks  11th Floor Lecture Hall

11:05  11:15 am ESTShixuan Zhang IntroductionLightning Talks  11th Floor Lecture Hall

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Friday, February 10, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Monday, February 13, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Tuesday, February 14, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

9:00  10:00 am ESTProfessional Development: Ethics IProfessional Development  11th Floor Lecture Hall

10:30  11:15 am ESTSemialgebraic parametric analysis by metaprogramming and applications in optimization.Seminar  11th Floor Lecture Hall
 Yuan Zhou, University of Kentucky
Abstract
We develop a metaprogramming technique that transforms algebraic programs for testing a property for a given input parameter into programs that compute the parameter region (proofcell) of the input for which the property holds. The obtained proofcells are semialgebraic sets. We borrow techniques from global optimization for the simplification and representation of proofcells, and we investigate strategies that lead to shorter proofs. We discuss a few applications of the SPAM technique to portfolio optimization, solving multiparametric mixedinteger programs and automated proofs of cutting plane theorems.

11:15 am  12:00 pm ESTThe Euclidean Steiner Problem.Seminar  11th Floor Lecture Hall
 Marcia Fampa, Federal University of Rio de Janeiro
Abstract
The Euclidean Steiner tree problem asks for a network of minimum length interconnecting a given set of points in ndimensional Euclidean space. We present a historical background for this problem, discuss mathematical programming models and algorithms to solve it, and identify characteristics of the problem that make its solution a big challenge when n is greater than 2.

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Wednesday, February 15, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Thursday, February 16, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

2:00  2:30 pm ESTIntroduction to the Circuits of Polyhedra: Basics, Diameters, and OptimizationPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
 Sean Kafer, University of Waterloo
Abstract
This talk will serve as a groundup introduction to the topic of circuits of polyhedra. The circuits are a set of directions associated with a given polyhedron which generalize the set of its edgedirections. As such, they are studied for their relevance to diameters of polyhedra, as well as to linear optimization. We will discuss the fundamental properties of circuits that motivate their usefulness, and we will look at the circuits of the matching and fractional matching polytopes as a concrete example. We will then introduce the circuit diameter  a generalization of the combinatorial diameter  discuss the ways in which the circuit diameter differs substantially from the combinatorial diameter, and introduce some results on the topic. Finally, we will discuss some ways in which circuits have been applied to the topic of linear optimization.

2:30  3:00 pm ESTDynamic Programming and the Knapsack ProblemPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
 Juan Carlos Martinez Mori, Cornell University
Abstract
In this selfcontained talk, I will explain a dynamic programming approach to solve the Knapsack Problem in pseudopolynomial time due to Lawler. Then, I will explain how to turn this approach into a fully polynomialtime approximation scheme (FPTAS), which is to say that its running time depends polynomially on the desired approximation precision. This technique, due to Ibarra and Kim, is a classical example of the rounding data approach in dynamic programming.

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Friday, February 17, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Tuesday, February 21, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

9:00  10:00 am ESTProfessional Development: Ethics IIProfessional Development  11th Floor Lecture Hall

10:30  11:15 am ESTPolynomial upper bounds on the number of differing columns of $\Delta$modular integer programsSeminar  11th Floor Lecture Hall
 Luze Xu, University of California, Davis
Abstract
We study integervalued matrices with bounded determinants. Such matrices appear in the theory of integer programs (IP) with bounded determinants. One of the first works about the structure of the matrix with bounded determinants was that of Heller, who identified the maximum number of differing columns in a totally unimodular matrix. Each extension of Heller's bound to general determinants has been superpolynomial in the determinants or the number of equations. We provide the first column bound that is polynomial in both values. Furthermore, we show a tight bound on the number of differing columns in a bimodular matrix; this is the first tight bound since Heller. Our analysis reveals combinatorial properties of bimodular IPs that may be of independent interest.

11:15 am  12:00 pm ESTOn circuit imbalance measures and their role in linear programmingSeminar  11th Floor Lecture Hall
 Bento Natura, Georgia Tech
Abstract
The geometry of polytopes as well as the efficiency of many algorithms for linear programs depends on certain condition numbers of the constraint matrix. We study the circuit imbalance measure, which bounds the ratio of nonzero entries of supportminimal nonzero vectors in the kernel of the constraint matrix. We further prove stronger upper bounds on circuit diameter and the iteration complexity of circuit augmentation schemes.

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Wednesday, February 22, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Thursday, February 23, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

2:00  3:00 pm ESTMaximum Entropy Sampling: Introduction and ComplexityPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
 Hessa AlThani, University of Michigan
 Zhongzhu Chen, University of Michigan
Abstract
The problem of maximumentropy sampling (MESP) is a fundamental and highly challenging combinatorial optimization problem that finds its applications in spatial statistics. In this talk we will introduce the problem, talk about some techniques that reduce the upper bound and we will also look at the NPhardness of different classes of the MESP. The MESP’s objective is to identify a maximumdeterminant orders principal submatrix of an ordern covariance matrix (C). Due to its NPhard complexity, exact solutions to MESP rely on a branchandbound (B&B) framework. To ensure efficient computation using the B&B technique, it is necessary to establish tight upper bounds for the optimal value of MESP. We present a range of techniques that can enhance both current and future upper bounds of MESP. These techniques operate on the principle that the optimal value of MESP remains unaffected by them, while the upper bounds are highly sensitive to their application. For certain classes of the input C we can find exact algorithms that solve the MESP. This is the case when C is tridiagonal or when C’s support graph is a spider. For both cases we will present a dynamic programming algorithm that solves the MESP. We will also present and discuss some classes of C where the MESP is NPHard.

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Friday, February 24, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:00  3:30 pm ESTCoffee Break11th Floor Collaborative Space
Monday, February 27, 2023

8:50  9:00 am ESTWelcome11th Floor Lecture Hall
 Brendan Hassett, ICERM/Brown University

9:00  9:45 am ESTOn Constrained MixedInteger DRSubmodular Minimization11th Floor Lecture Hall
 Speaker
 Simge Küçükyavuz, Northwestern University
 Session Chair
 Jon Lee, University of Michigan
Abstract
Diminishing Returns (DR)submodular functions encompass a broad class of functions that are generally nonconvex and nonconcave. We study the problem of minimizing any DRsubmodular function, with continuous and general integer variables, under box constraints and possibly additional monotonicity constraints. We propose valid linear inequalities for the epigraph of any DRsubmodular function under the constraints. We further provide the complete convex hull of such an epigraph, which, surprisingly, turns out to be polyhedral. We propose a polynomialtime exact separation algorithm for our proposed valid inequalities, with which we first establish the polynomialtime solvability of this class of mixedinteger nonlinear optimization problems. This is joint work with Kim Yu.

10:00  10:30 am ESTCoffee Break11th Floor Collaborative Space

10:30  11:15 am ESTSemidefinite Optimization with Eigenvector Branching11th Floor Lecture Hall
 Speaker
 Kurt Anstreicher, University of Iowa
 Session Chair
 Jon Lee, University of Michigan
Abstract
Semidefinite programming (SDP) problems typically utilize the constraint that Xxx' is positive semidefinite to obtain a convex relaxation of the condition X=xx', where x is an nvector. We consider a new hyperplane branching method for SDP based on using an eigenvector of Xxx'. This branching technique is related to previous work of Saxeena, Bonami and Lee who used such an eigenvector to derive a disjunctive cut. We obtain excellent computational results applying the new branching technique to difficult instances of the twotrustregion subproblem.

11:30 am  12:15 pm ESTA Breakpoints Based Method for the Maximum Diversity and Dispersion Problems11th Floor Lecture Hall
 Speaker
 Dorit Hochbaum, University of California, Berkeley
 Session Chair
 Jon Lee, University of Michigan
Abstract
The maximum diversity, or dispersion, problem (MDP), is to select from a given set a subset of elements of given size (budget), so that the sum of pairwise distances, or utilities, between the selected elements is maximized. We introduce here a method, called the Breakpoints (BP) algorithm, based on a technique proposed in Hochbaum (2009), to generate the concave piecewise linear envelope of the solutions to the relaxation of the problem for all values of the budget. The breakpoints in this envelope are provably optimal for the respective budgets and are attained using a parametric cut procedure that is very efficient. The problem is then solved, for any given value of the budget, by applying a greedylike method to add or subtract nodes from adjacent breakpoints. This method works well if for the given budget there are breakpoints that are ``close". However, for many data sets and budgets this is not the case, and the breakpoints are sparse. We introduce a perturbation technique applied to the utility values in cases where there is paucity of breakpoints, and show that this results in denser collections of breakpoints. Furthermore, each optimal perturbed solution is quite close to an optimal nonperturbed solution. We compare the performance of our breakpoints algorithm to leading methods for these problems: The metaheuristic OBMA, that was shown recently to perform better than GRASP, Neighborhood search and Tabu Search, and Gurobian integer programming software. It is demonstrated that our method dominates the performance of these methods in terms of computation speed and in comparable or better solution quality.

12:30  2:30 pm ESTLunch/Free Time

2:30  3:15 pm ESTApproximating integer programs with monomial orders11th Floor Lecture Hall
 Virtual Speaker
 Akshay Gupte, University of Edinburgh
 Session Chair
 Dorit Hochbaum, University of California, Berkeley
Abstract
We consider the problem of maximizing a function over integer points in a compact set. Inner and outerapproximations of the integer feasible set are obtained using families of monomial orders over the integer lattice. The convex hull is characterized when the monomial orders satisfy some properties. When the objective function is submodular or subadditive, we provide a theoretical guarantee on the quality of the innerapproximations in terms of their gap to the optimal value. An algorithm is proposed to generate feasible solutions, and it is competitive with a commercial solver in numerical experiments on benchmark test instances for integer LPs.

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm ESTSolving ACOPF problems11th Floor Lecture Hall
 Speaker
 Daniel Bienstock, Columbia University
 Session Chair
 Dorit Hochbaum, University of California, Berkeley
Abstract
In this talk we will detail our recent experience in solving the ACOPF problem, a notorious MINLP. We will do this from two perspectives. First, we will detail our experience in the recent, and ongoing GO competition for solving modern, largescale versions of ACOPF which include scenario constraints and integer variables. Second, we will outline challenges to stateoftheart MINLP solvers based on spatial branchandbound that arise in ACOPF instances. Finally we will discuss some fundamental issues related to numerical precision.

5:00  6:30 pm ESTReception11th Floor Collaborative Space
Tuesday, February 28, 2023

9:00  9:45 am ESTMaximal quadratic free sets: basic constructions and steps towards a full characterization11th Floor Lecture Hall
 Speaker
 Gonzalo Muñoz, Universidad de O'Higgins
 Session Chair
 Daniel Bienstock, Columbia University
Abstract
In 1971, Balas introduced intersection cuts as a method for generating cutting planes in integer optimization. These cuts are derived from convex Sfree sets, and inclusionwise maximal Sfree sets yield the strongest intersection cuts. When S is a lattice, maximal Sfree sets are wellstudied from theoretical and computational standpoints. In this talk, we focus on the case when S is defined by a general quadratic inequality and show how to construct basic maximal quadraticfree sets. Additionally, we explore how to generalize the basic procedure to construct a plethora of new maximal quadraticfree sets for homogeneous quadratics. Joint work with Joseph Paat and Felipe Serrano.

10:00  10:30 am ESTCoffee Break11th Floor Collaborative Space

10:30  11:15 am ESTFrom micro to macro structure: a journey in company of the Unit Commitment problem11th Floor Lecture Hall
 Speaker
 Antonio Frangioni, Università di Pisa
 Session Chair
 Daniel Bienstock, Columbia University
Abstract
The fact that "challenging problems motivate methodological advances", as obvious as it may seem, is nonetheless very true. I was drawn long ago to Unit Commitment problems because of a specific methodology, but studying it led us to interesting results for entirely different ones. This talk will summarise on (the current status of) a long journey of discovery that ebbed and flowed between different notions of structure, starting from the "macro" one of spatial decomposition and its algorithmic implications, descending to the "micro" one of the Perspective Reformulation of tiny fragments of the problem, putting both back together to fullproblem size with the definition of strong but large formulations (and the nontrivial tradeoffs they entail), and finally skyrocketing to large and hugescale problems (stochastic UC, stochastic reservoirs optimization, longterm energy system design) where UC (and its substructures) is but one of the multiple nested forms of structure. The talk will necessarily have to focus on a few of the results that hopefully have broader usefulness than just UC, among which a recent one on the Convex Hull of StarShaped MINLPs, but it will also try to give a broadbrush of the larger picture, with some time devoted to discussing the nontrivial implications of actually implementing solution methods for hugescale problems with multiple nested form of heterogeneous structure and the (surely partial and tentative) attempts at tackling these issues within the SMS++ modelling system.

11:30 am  12:15 pm ESTA fast combinatorial algorithm for the bilevel knapsack interdiction problem11th Floor Lecture Hall
 Speaker
 Ricardo Fukasawa, University of Waterloo
 Session Chair
 Daniel Bienstock, Columbia University
Abstract
The singlelevel (classical) knapsack problem consists of picking a subset of n items maximizing profit, subject to a budget (knapsack) constraint. In the bilevel knapsack interdiction problem, there are two levels of decisionmakers. The lowerlevel decision maker is attempting to solve the classical knapsack problem. The upperlevel decision maker has the goal of minimizing the profit of the lowerlevel decision maker, by picking items that will be then unavailable. The upperlevel has its own (independent) knapsack constraint to satisfy too. Previous approaches to this problem were based on using MIP solvers. We develop a branchandbound algorithm for the problem that relies on a strong lower bound and specialized branching, using combinatorial arguments. Our approach improves on the previous best approaches by up to two orders of magnitude in our test instances, significantly increasing the size of instances that can be consistently solved to optimality. This is joint work with Noah Weninger.

12:30  2:30 pm ESTLunch/Free Time

2:30  3:15 pm ESTNetwork Design Queueing MINLP: Models, Reformulations, and Algorithms11th Floor Lecture Hall
 Speaker
 Miguel Lejeune, George Washington University
 Session Chair
 Merve Bodur, University of Toronto
Abstract
We present several queueingbased optimization models to design networks in which the objective is to minimize the response time. The networks are modelled as collections of interdependent M/G/1 or M/G/K queueing systems with fixed and mobile servers. The optimization models take the form of nonconvex MINLP problems with fractional and bilinear terms. We derive a reformulation approach and propose a solution method that features a warmstart component, new optimalitybased bound tightening (OBBT) techniques, and an outer approximation algorithm. In particular, we propose new MILP and feasibility OBBT models that can derive multiple variable bounds at once. The proposed approach is applied to the dronebased delivery of automated external defibrillators to outofhospital cardiac arrests (OHCA) and naloxone to opioid overdoses. The computational experiments are based on reallife data from Virginia Beach, and ascertain the computational efficiency of the approach and its impact on the response time and the probability of survival of patients.

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm ESTIntegrated Computational and Experimental Research in Mixed Integer Programming with SageMath11th Floor Lecture Hall
 Virtual Speaker
 Matthias Köppe, UC Davis
 Session Chair
 Merve Bodur, University of Toronto
Abstract
I will introduce SageMath, a generalpurpose, Pythonbased, opensource mathematics system in development since 2005, from the viewpoint of its use in Mixed Integer Programming research. Originally conceived as a computer algebra system focused on algebraic number theory, SageMath has grown to a major integrating force in the mathematical software world that provides convenient and unified access to the best libraries and systems for polyhedral geometry, mixed integer linear programming, lattices, graph theory, commutative algebra, symbolic computation, computational group theory, and more. I will demonstrate some of these capabilities. The SageMath community welcomes contributions in the form of expository mathematical writing, constructions, algorithm development and implementation, cataloging, mathematical software integration, and more. I will highlight some possible entry points for making such contributions.
Wednesday, March 1, 2023

9:00  9:45 am ESTMinimizing quadratics over integers11th Floor Lecture Hall
 Speaker
 Alberto Del Pia, University of WisconsinMadison
 Session Chair
 Nick Sahinidis, Georgia Institute of Technology
Abstract
Mixed integer quadratic programming is the problem of minimizing a quadratic polynomial over points in a polyhedral region with some integer components. It is a natural extension of mixed integer linear programming and it has a wide array of applications. In this talk, I will survey some recent theoretical developments in mixed integer quadratic programming, with a focus on complexity, algorithms, and fundamental properties.

10:00  10:30 am ESTCoffee Break11th Floor Collaborative Space

10:30  11:15 am ESTOptimizing for Equity in Urban Planning11th Floor Lecture Hall
 Speaker
 Emily Speakman, University of Colorado  Denver
 Session Chair
 Nick Sahinidis, Georgia Institute of Technology
Abstract
In the Environmental Justice literature, the KolmPollak Equally Distributed Equivalent (EDE) is the preferred metric for quantifying the experience of a population. The metric incorporates both the center and the spread of the distribution of the individual experiences, and therefore, captures the experience of an “average” individual more accurately than the population mean. In particular, the mean is unable to measure the equity of a distribution, while the KolmPollak EDE is designed to penalize for inequity. In this talk, we explore the problem of finding an optimal distribution from various alternatives using the KolmPollak EDE to quantify optimal. Unfortunately, optimizing over the KolmPollak EDE in a mathematical programming model is not trivial because of the nonlinearity of the function. We discuss methods to overcome this difficulty and present computational results for practical applications. Our results demonstrate that optimizing over the KolmPollak EDE in a standard facility location model has the same computational burden as optimizing over the population mean. Moreover, it often results in solutions that are significantly more equitable while having little impact on the mean of the distribution, versus optimizing over the mean directly. Joint work with Drew Horton, Tom Logan, and Daphne Skipper

11:30 am  12:15 pm ESTExplicit convex hull description of bivariate quadratic sets with indicator variables11th Floor Lecture Hall
 Speaker
 Aida Khajavirad, Lehigh University
 Session Chair
 Nick Sahinidis, Georgia Institute of Technology
Abstract
We obtain an explicit description for the closure of the convex hull of bivariate quadratic sets with indicator variables the space of original variables. We present a simple separation algorithm that can be incorporated in branchandcut based solvers to enhance the quality of existing relaxations.

12:25  12:30 pm ESTGroup Photo (Immediately After Talk)11th Floor Lecture Hall

12:30  2:30 pm ESTNetworking LunchLunch/Free Time  11th Floor Collaborative Space

2:30  3:30 pm EST

3:30  4:00 pm ESTCoffee Break10th Floor Collaborative Space

4:00  4:45 pm ESTMatrix Completion over GF(2) with Applications to Index Coding11th Floor Lecture Hall
 Speaker
 Jeff Linderoth, University of WisconsinMadison
 Session Chair
 Kurt Anstreicher, University of Iowa
Abstract
We discuss integerprogrammingbased approaches to doing lowrank matrix completion over the finite field of two elements. We are able to derive an explicit description for the convex hull of an individual matrix element in the decomposition, using this as the basis of a new formulation. Computational results showing the superiority of the new formulation over a natural formulation based on McCormick inequalities with integervalued variables, and an extended disjunctive formulation arising from the parity polytope are given in the context of linear index coding.
Thursday, March 2, 2023

9:00  9:45 am ESTDantzigWolfe Bound by Cutting Planes11th Floor Lecture Hall
 Speaker
 Oktay Gunluk, Cornell University
 Session Chair
 Yuan Zhou, University of Kentucky
Abstract
DantzigWolfe (DW) decomposition is a wellknown technique in mixedinteger programming for decomposing and convexifying constraints to obtain potentially strong dual bounds. We investigate Fenchel cuts that can be derived using the DW decomposition algorithm and show that these cuts can provide the same dual bounds as DW decomposition. We show that these cuts, in essence, decompose the objective function cut one can simply write using the DW bound. Compared to the objective function cut, these Fenchel cuts lead to a formulation with lower dual degeneracy, and consequently a better computational performance under the standard branchandcut framework in the original space. We also discuss how to strengthen these cuts to improve the computational performance further. We test our approach on the Multiple Knapsack Assignment Problem and show that the proposed cuts are helpful in accelerating the solution time without the need to implement branch and price.

10:00  10:30 am ESTCoffee Break11th Floor Collaborative Space

10:30  11:15 am ESTNumber of inequalities in integerprogramming descriptions of a set11th Floor Lecture Hall
 Virtual Speaker
 Gennady Averkov, Brandeburg Technical University
 Session Chair
 Yuan Zhou, University of Kentucky
Abstract
I am going to present results obtained jointly with Manuel Aprile, Marco Di Summa, Christopher Hojny and Matthias Schymura. Assume you want to describe a set X of integer points as the set of integer solutions of a linear system of inequalities and you want to use a system for X with the minimum number of inequalities. Can you compute this number algorithmically? The answer is not known in general! Does the choice of the coefficient field (like the field of real and the fiel of rational numbers) have any influence on the number you get as the answer? Surprisingly, it does! On a philosophical level, should we do integer programming over the rationals or real coefficients? That's actually not quite clear, but for some aspects there is a difference so that it might be interesting to reflect on this point and weigh pros and cons.

11:30 am  12:15 pm EST2x2Convexifications for Convex Quadratic Optimization with Indicator Variables11th Floor Lecture Hall
 Speaker
 Alper Atamturk, University of California  Berkeley
 Session Chair
 Yuan Zhou, University of Kentucky
Abstract
In this talk, we present new strong relaxations for the convex quadratic optimization problem with indicator variables. For the bivariate case, we describe the convex hull of the epigraph in the original space of variables, and also give a conic quadratic extended formulation. Then, using the convex hull description for the bivariate case as a building block, we derive an extended SDP relaxation for the general case. This new formulation is stronger than other SDP relaxations proposed in the literature for the problem, including Shor's SDP relaxation, the optimal perspective relaxation as well as the optimal rankone relaxation. Computational experiments indicate that the proposed formulations are quite effective in reducing the integrality gap of the optimization problems. This is a joint work with Shaoning Han and Andres Gomez.

12:30  2:30 pm ESTLunch/Free Time

2:30  3:15 pm ESTInteger Semidefinite Programming  a New Perspective11th Floor Lecture Hall
 Speaker
 Renata Sotirov, Tilburg University
 Session Chair
 Fatma KılınçKarzan, Carnegie Mellon University
Abstract
Integer semidefinite programming can be viewed as a generalization of integer programming where the vector variables are replaced by positive semidefinite integer matrix variables. The combination of positive semidefiniteness and integrality allows to formulate various optimization problems as integer semidefinite programs (ISDPs). Nevertheless, ISDPs have received attention only very recently. In this talk we show how to extend the Chv\'atalGomory (CG) cuttingplane procedure to ISDPs. We also show how to exploit CG cuts in a branchandcut framework for ISDPs. Finally, we demonstrate the practical strength of the CG cuts in our branchandcut algorithm. Our results provide a new perspective on ISDPs.

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm ESTReciprocity between tree ensemble optimization and multilinear optimization11th Floor Lecture Hall
 Speaker
 Mohit Tawarmalani, Purdue University
 Session Chair
 Fatma KılınçKarzan, Carnegie Mellon University
Abstract
We establish a polynomial equivalence between tree ensemble optimization and optimization of multilinear functions over the Cartesian product of simplices. Using this, we derive new formulations for tree ensemble optimization problems and obtain new convex hull results for multilinear polytopes. A computational experiment on multicommodity transportation problems with costs modeled using tree ensembles shows the practical advantage of our formulation relative to existing formulations of tree ensembles and other piecewiselinear modeling techniques. We then consider piecewise polyhedral relaxation of multilinear optimization problems. We provide the first ideal formulation over nonregular partitions. We also improve the relaxations over regular partitions by adding linking constraints. These relaxations significantly improve performance of ALPINE and are included in the software.
This is joint work with Jongeun Kim (Google) and J.P. P. Richard (University of Minnesota).
Friday, March 3, 2023

9:00  9:45 am ESTMarkov Chainbased Policies for Multistage Stochastic Integer Linear Programming11th Floor Lecture Hall
 Speaker
 Merve Bodur, University of Toronto
 Session Chair
 Pietro Belotti, Politecnico di Milano
Abstract
We introduce a novel aggregation framework to address multistage stochastic programs with mixedinteger state variables and continuous local variables (MSILPs). Our aggregation framework imposes additional structure to the integer state variables by leveraging the information of the underlying stochastic process, which is modeled as a Markov chain (MC). We present a novel branchandcut algorithm integrated with stochastic dual dynamic programming as an exact solution method to the aggregated MSILP, which can also be used in an approximation form to obtain dual bounds and implementable feasible solutions. Moreover, we apply twostage linear decision rule (2SLDR) approximations and propose MCbased variants to obtain highquality decision policies with significantly reduced computational effort. We test the proposed methodologies in a novel MSILP model for hurricane disaster relief logistics planning.

10:00  10:30 am ESTCoffee Break11th Floor Collaborative Space

10:30  11:15 am ESTOn practical first order methods for LP11th Floor Lecture Hall
 Speaker
 Daniel Espinoza, Google Research
 Session Chair
 Pietro Belotti, Politecnico di Milano
Abstract
Solving linear programs is nowadays an everyday task. Used even in embedded systems, but also run on very large hardware. However, solving very large models has remained a major challenge. Either because most successful algorithms require more than linear space to solve such models, or because they become extremely slow in practice. Although the concept of first ordermethods, and potential function methods have been around for a long time, they have failed to be broadly applicable, or no competitive implementations are widely available. In this talk we will be motivating the need for such a class of algorithms, share some (known) evidence that such schemes have worked in special situations, and present results of experiments running one such algorithm (PDLP) both in standard benchmark models, and also on very large models arising from network planning. And also on a first order method for general LPs using an exponential potential function to deal with unstructured constraints.

11:30 am  1:30 pm ESTLunch/Free Time

1:30  2:15 pm ESTIdeal polyhedral relaxations of nonpolyhedral sets11th Floor Lecture Hall
 Speaker
 Andres Gomez, University of Southern California
 Session Chair
 Marcia Fampa, Federal University of Rio de Janeiro
Abstract
Algorithms for mixedinteger optimization problems are based on the sequential construction of tractable relaxations of the discrete problem, until the relaxations are sufficiently tight to guarantee optimality of the resulting solution. For classical operational and logistics problems, which can be formulated as mixedinteger linear optimization problems, it is wellknown that such relaxations should be polyhedral. Thus, there has been a sustained stream of research spanning several decades on constructing and exploiting linear relaxations. As a consequence, mixedinteger linear optimization problems deemed to be intractable 30 years old can be solved to optimality in seconds or minutes nowadays. Modern statistical and decisionmaking problems call for mixedinteger nonlinear optimization (MINLO) formulations, which inherently lead to nonpolyhedral relaxations. There has been a substantial progress in extending and adapting techniques for both the mixedinteger linear optimization and continuous nonlinear literatures, but there may a fundamental limit on the effectiveness of such approaches as they fail to exploit the specific characteristics of MINLO problems. In this talk, we discuss recent progress in studying the fundamental structure of MINLO problems. In particular, we show that such problems have a hidden polyhedral substructure that captures the nonconvexities associated with discrete variables. Thus, by exploiting this substructure, convexification theory and methods based on polyhedral theory can naturally be used study nonpolyhedral sets. We also provide insights into how to design algorithms that tackle the ensuing relaxations.

2:30  3:15 pm ESTOn DantzigWolfe Relaxation of Rank Constrained Optimization: Exactness, Rank Bounds, and Algorithms11th Floor Lecture Hall
 Speaker
 Weijun Xie, Georgia Institute of Technology
 Session Chair
 Marcia Fampa, Federal University of Rio de Janeiro
Abstract
This paper studies the rank constrained optimization problem (RCOP) that aims to minimize a linear objective function over intersecting a prespecified closed rank constrained domain set with twosided linear matrix inequalities. The generic RCOP framework exists in many nonconvex optimization and machine learning problems. Although RCOP is, in general, NPhard, recent studies reveal that its DantzigWolfe Relaxation (DWR), which refers to replacing the domain set by its closed convex hull, can lead to a promising relaxation scheme. This motivates us to study the strength of DWR. Specifically, we develop the firstknown necessary and sufficient conditions under which the DWR and RCOP are equivalent. Beyond the exactness, we prove the rank bound of optimal DWR extreme points. We design a column generation algorithm with an effective separation procedure. The numerical study confirms the promise of the proposed theoretical and algorithmic results.

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Monday, March 6, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Tuesday, March 7, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

10:30  11:15 am ESTSmall simplicial spheres of large diameterSeminar  11th Floor Lecture Hall
 Francisco Criado Gallart, CUNEF Universidad
Abstract
In this talk we study the topological version of the Hirsch conjecture. In this topological setting, we do not study the diameter of polyhedral graphs, rather we study what is the diameter of the dual graph of a triangulation of the sphere. This is motivated by Klee's remark: We need more examples of polytopes not satisfying the Hirsch bound to understand what makes a polytope nonHirsch. Our approach uses computerguided search to explore a large collection of nonHirsch simplicial spheres, and uses simulated annealing to find the smallest topological examples yet: 8dimensional simplicial spheres with 18 vertices exceeding the Hirsch bound. We do not know if any of these are polytopal yet. Reference: https://arxiv.org/abs/1807.03030

11:15 am  12:00 pm ESTNew Algorithmic Results for Scheduling via ILPsSeminar  11th Floor Lecture Hall
 Klaus Jansen, Kiel University
Abstract
In this talk we present an overview about new results for scheduling problems on identical machines. During the last years we have worked on the design of efficient exact and approximation algorithms for packing and scheduling problems. In order to obtain faster (implementable) algorithms we studied integer linear programming (ILP) formulations for these problems, developed new parameterized algorithms based on the Steinitz lemma and discrepancy bounds, and proved structural results for optimum solutions of the corresponding ILPs and lower bounds on the running time. This is joint work with Sebastian Berndt, Lin Chen, Max Deppert, KimManuel Klein, Lars Rohwedder, José Verschae, and Gouchuan Zhang.

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Wednesday, March 8, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Thursday, March 9, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

2:00  2:30 pm ESTIntroduction to Iterative Methods in Combinatorial OptimizationPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
 Shubhang Kulkarni, University of Illinois, UrbanaChampaign
Abstract
This talk will be an introduction to the iterated rounding/relaxation framework in combinatorial optimization. At a highlevel, iterated rounding/relaxation is an algorithmic technique where one tries to leverage extreme point properties of polyhedra via the following general iterative procedure: at every iteration, (1) obtain an extreme point solution to an LP for the problem instance, (2) round a subset of the variables based on extreme point properties, (3) relax a subset of the constraints, (4) update the problem instance based on the rounded variables and relaxed constraints. I will introduce the algorithmic technique by focusing on the familiar problem of finding the minimumcost spanning tree in an undirected graph. Here, I will introduce the uncrossing and the (fractional) tokencounting methods. Then, I will show how to extend these ideas to get an additive approximation algorithm for the NPhard degreebounded minimumcost spanning tree problem. I will conclude the talk with some open questions in the area.

2:30  3:00 pm ESTBatched Dueling BanditsPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
 Rohan Ghuge, University of Michigan
Abstract
In this talk, we discuss the Karmed dueling bandits problem, a variation of the multiarmed bandit problem where the feedback is in the form of noisy pairwise comparisons. This problem has applications in a widevariety of domains like search ranking, recommendation systems and sports ranking where eliciting qualitative feedback is easy while realvalued feedback is not easily interpretable. Previous works have only focused on the sequential setting where the learning policy adapts after every comparison. However, in many applications such as search ranking and recommendation systems, it is preferable to perform comparisons in a limited number of parallel batches. We introduce and study the batched dueling bandits problem, for which we design algorithms with a smooth tradeoff between the number of batches and regret.

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Friday, March 10, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm ESTCoffee Break11th Floor Collaborative Space
Monday, March 13, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, March 14, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

10:30  11:15 am EDTMILPs to optimally select publicfunded R&D projectsSeminar  11th Floor Lecture Hall
 Nancy Maribel Arratia Martinez, Universidad de las Américas Puebla
Abstract
In this talk, I present the problem of portfolio selection of research and development (R&D) projects supported by public funds. I review the different problem classes, the stateoftheart techniques to solve them, and the most recent applications. In particular, I discuss problems that involve inaccurate information in the portfolio selection. To this end, I explore fuzzy logic and fuzzy numbers to tackle the particular challenges of these problems. I conduct numerical experiments to explore the performance of methods applied in terms of solution quality and computing time. I conclude the talk with a discussion of these methods and open problems in portfolio selection of publicfunded R&D projects.

11:15 am  12:00 pm EDTNeural networks with linear threshold activations: structure and algorithmsSeminar  11th Floor Lecture Hall
 Sammy Khalife, Johns Hopkins University
Abstract
(Joint work with Hongyu Cheng and Amitabh Basu)
In this talk I will present new results on neural networks with linear threshold activation functions. The class of functions that are representable by such neural networks can be fully characterized, and two hidden layers are necessary and sufficient to represent any function in the class. This is a surprising result in the light of recent exact representability investigations for neural networks using other popular activation functions like rectified linear units. I will present nearly tight bounds on the sizes of the neural network, as well as an algorithm to solve the empirical risk minimisation (ERM) problem to global optimality for these neural networks with a fixed architecture. The algorithm’s running time is polynomial in the size of the data sample, if the input dimension and the size of the network architecture are considered fixed constants. Finally I will present a new type of architecture, the shortcut linear threshold networks, a strict superclass of the rectified linear units (ReLU) neural networks, which has several desirable theoretical properties. In particular, the ERM problem can also be solved to global optimality with a similar algorithm. 
12:30  1:00 pm EDTPI DAY Coffee BreakCoffee Break  11th Floor Collaborative Space
Wednesday, March 15, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, March 16, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

2:00  2:30 pm EDTWhat the heck is a graphical design?Post Doc/Graduate Student Seminar  11th Floor Lecture Hall
 Catherine Babecki, University of Washington, Seattle
Abstract
A graphical design is a quadrature rule for a graph inspired by classical numerical integration on the sphere. Broadly speaking, that means a graphical design is a relatively small subset of graph vertices chosen to capture the global behavior of functions from the vertex set to the real numbers. I will motivate and define graphical designs for graphs with positive edge weights. Time permitting, I will explain a combinatorial bijection between graphical designs and the faces of certain polytopes associated to a graph that arises through Gale duality.

2:30  3:00 pm EDTSDP hierarchies for volume computationPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
 Chiara Meroni, ICERM
Abstract
How can we compute the volume of a semialgebraic set? There is a series of works by Henrion, Lasserre, and coauthors, in which they formulate the problem as an infinitedimensional LP, and introduce a hierarchy of SDP relaxations. I will give you an overview of the content, show some experiments, and illustrate a trick to speed the implementation. The validity of this trick is proved in some case, but still open in others. For notes to go with the talk, see the following link: https://9c12286303c54d209f29cc3a6fed5770.filesusr.com/ugd/1eacd3_f4b6fa4a558b474c9f00bb0e612115a4.pdf

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Friday, March 17, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Monday, March 20, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, March 21, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

9:00  10:00 am EDTProfessional Development: Hiring ProcessProfessional Development  11th Floor Lecture Hall

10:30  11:15 am EDTMemoryefficient approximation algorithm for SDPs and its application to MaxCut, MaxkCut, and Correlation ClusteringSeminar  11th Floor Lecture Hall
 Nimita Shinde, ICERM, Brown University
Abstract
Semidefinite programs (SDPs) are a special class of convex optimization problems that have a wide range of applications in areas such as control theory, statistical modeling, correlation clustering, community detection, angular synchronization, and combinatorial optimization. We discuss three fundamental graph partitioning problems MaxCut, MaxkCut, and the MaxAgree variant of correlation clustering. Given a graph G = (V, E), MaxkCut aims to divide the nodes into k partitions such that the weight of the edges crossing the partitions is maximized. MaxCut is a special case of MaxkCut with k = 2. While MaxAgree requires additional information about the ‘similarity’ or ‘dissimilarity’ of each pair of nodes (i, j) in E, and seeks to cluster the nodes of the graph such that the sum of the ‘similar’ edges within the cluster and ‘dissimilar’ edges across the clusters is maximized. For largescale instances of problems, the memory required to solve SDPs becomes a key computational bottleneck. We review a Gaussian samplingbased technique that replaces the decision variable of SDP with a zeromean Gaussian random vector whose covariance is equal to the value of the decision variable. This leads to a FrankWolfe based algorithmic framework that tracks the random vectors instead of the matrix iterates. We then apply this technique to the three combinatorial optimization problems, MaxCut, MaxkCut, and MaxAgree. We show that the proposed algorithmic framework uses O(V  + E) memory and generates an approximate solution to the input problem in polynomial time that nearly achieves the best existing approximation guarantees.

11:15 am  12:00 pm EDTBurerMonteiro lowrank optimization for sumofsquare certification11th Floor Lecture Hall
 Shixuan Zhang, Brown University
Abstract
To certify a sum of $k$ squares on a real projective variety, one can minimize the distance of the sum of squares of $k$ linear forms from it in the space of quadrics. When $k$ is smaller than the dimension of linear forms, the certification problem can be applied in lowrank semidefinite relaxation of polynomial optimization, dual to the BurerMonteiro method. In this talk, we give some preliminary results on the existence of spurious stationary points in this certification problem by explicit examples and some further study on their structure when the varieties have minimal degrees. For general varieties, we propose algorithmic remedies that guarantee the convergence to global minima.

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, March 22, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTMentoring Coffee / TeaCoffee Break  11th Floor Collaborative Space
Thursday, March 23, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

2:00  2:30 pm EDTFourier on convex compact bodies: Siegel meets MinkowskiPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
 Sammy Khalife, Johns Hopkins University
Abstract
In 1889, Minkowski provided a sufficient and necessary condition for a symmetric convex body K in R^d to contain an integral point in its interior, given by Vol(K) > 2^{d}. After introducing the relevant facts in Fourier Analysis, I will discuss how one can use them to get a stronger statement expressing the gap between Vol(K) and 2^{d} in general. These results can be easily extended to intersection with Lattices and to K being compact. An application will be to deduce an original characterization of the extremal bodies, i.e. convex symmetric bodies such that Vol(K)=2^d. They correspond to the bodies which, when scaled by half, tile R^d after translations by the integral points.

2:30  3:00 pm EDTPPAD hardness – the complexity of Nash equilibriumPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
 Chengyue He, Columbia University
Abstract
PPAD is a class of search problems where the solution is shown to exist by a parity argument. Whether a PPADcomplete problem admits a polytime algorithm raises significant attention in the algorithmic game theory community. We will present a brief introduction to this class by both discrete (Sperner’s lemma) and continuous (Brouwer fixed point theorem) perspectives. In addition, we will see how this relates to some famous results like Nash equilibrium, Scarf’s lemma and hypergraphic stable matching.

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Friday, March 24, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Monday, March 27, 2023

8:30  8:50 am EDTCheck In11th Floor Collaborative Space

8:50  9:00 am EDTWelcome11th Floor Lecture Hall
 Brendan Hassett, ICERM/Brown University

9:00  9:45 am EDTInterior point methods are not worse than Simplex11th Floor Lecture Hall
 Speaker
 Daniel Dadush, Centrum Wiskunde & Informatica
 Session Chair
 Jesús De Loera, University of California, Davis
Abstract
Whereas interior point methods provide polynomialtime linear programming algorithms, the running time bounds depend on bitcomplexity or condition measures that can be unbounded in the problem dimension. This is in contrast with the classical simplex method that always admits an exponential bound. We introduce a new polynomialtime pathfollowing interior point method where the number of iterations also admits a combinatorial upper bound O(2^n n^{1.5} log n) for an nvariable linear program in standard form. This complements previous work by Allamigeon, Benchimol, Gaubert, and Joswig (SIAGA 2018) that exhibited a family of instances where any pathfollowing method must take exponentially many iterations.
The number of iterations of our algorithm is at most O(n^{1.5} log n) times the number of segments of any piecewise linear curve in the wide neighborhood of the central path. In particular, it matches the number of iterations of any path following interior point method up to this polynomial factor. The overall exponential upper bound derives from studying the ‘max central path’, a piecewiselinear curve with the number of pieces bounded by the total length of n shadow vertex simplex paths.
This is joint work with Xavier Allamigeon (INRIA / Ecole Polytechnique), Georg Loho (U. Twente), Bento Natura (LSE), Laszlo Vegh (LSE). 
10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTPartitioning over submodular structures11th Floor Lecture Hall
 Speaker
 Karthekeyan Chandrasekaran, University of Illinois UrbanaChampaign
 Session Chair
 Jesús De Loera, University of California, Davis
Abstract
In submodular kpartitioning problems, the input is a submodular set function (given via an evaluation oracle) along with a fixed positive integer k (e.g., k = 2, 3, 4, …) and the goal is to partition the ground set into k nonempty parts so as to minimize certain natural objectives of interest. Submodular kpartitioning generalizes partitioning problems over several interesting structures including graphs and hypergraphs. The case of 2partitioning corresponds to the classic and wellstudied submodular minimization problem which is polynomialtime solvable. In this talk, I will outline recent progress towards polynomialtime solvability of submodular kpartitioning for fixed constant integers k >= 3.

11:30 am  12:15 pm EDTThe Polyhedral Structure of Graphical Designs11th Floor Lecture Hall
 Speaker
 Catherine Babecki, University of Washington, Seattle
 Session Chair
 Jesús De Loera, University of California, Davis
Abstract
A graphical design is a quadrature rule for a graph inspired by classical numerical integration on the sphere. Broadly speaking, that means a graphical design is a relatively small subset of graph vertices chosen to capture the global behavior of functions from the vertex set to the real numbers. We first motivate and define graphical designs for graphs with positive edge weights. Through Gale duality, we exhibit a combinatorial bijection between graphical designs and the faces of certain polytopes associated to a graph, called eigenpolytopes. This polytope connection has a variety of beautiful consequences, including a proof of existence, an upper bound on the cardinality of a graphical design, methods to compute, optimize, and organize graphical designs, the existence of random walks with improved convergence rates, and complexity results for associated computational problems. This talk is based on work with Rekha Thomas, Stefan Steinerberger and David Shiroma.

12:30  2:30 pm EDTLunch/Free Time

2:30  3:15 pm EDTTwo New Algorithms for Set Covering11th Floor Lecture Hall
 Speaker
 Anupam Gupta, Carnegie Mellon University
 Session Chair
 Yuri Faenza, Columbia University
Abstract
In the set covering problem we are given a set system, and we want to find a subcollection with few sets whose union is the entire universe. This problem is NPhard to approximate to better than (ln n). Moreover we know matching algorithms which are achieved by both greedy and relaxandround based algorithms. In this talk I will give two more algorithms which achieve the same guarantee (asymptotically), one based on local search, and another based on a learningbased framework (which also works in an online setting with random arrivals). These results are based on joint works with Greg Kehne, Euiwoong Lee, Roie Levin, and Jason Li.

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTAlternating Linear Minimization: Revisiting von Neumann’s alternating projections11th Floor Lecture Hall
 Speaker
 Sebastian Pokutta, Zuse Institute Berlin (ZIB)
 Session Chair
 Yuri Faenza, Columbia University
Abstract
In 1933 von Neumann proved a beautiful result that one can compute a point in the intersection of two convex sets (under suitable assumptions) by alternating projections, i.e., successively projecting on one set and then the other. This algorithm assumes that one has access to projection operators for both sets. Here we consider the much weaker setup where we have only access to linear minimization oracles over the convex sets and present an algorithm to find a point in the intersection of two convex sets. Moreover, we provide a modification of the algorithm to minimize a linear function over the intersection and discuss further extensions.

5:00  6:30 pm EDTReception11th Floor Collaborative Space
Tuesday, March 28, 2023

9:00  9:45 am EDTReusing Cuts in Iterative Projections over Submodular Polytopes11th Floor Lecture Hall
 Speaker
 Swati Gupta, Georgia Tech
 Session Chair
 Karthekeyan Chandrasekaran, University of Illinois UrbanaChampaign
Abstract
Optimization algorithms such as projected Newton's method, FISTA, mirror descent and its variants enjoy nearoptimal regret bounds and convergence rates, but suffer from a computational bottleneck of computing projections"" in potentially each iteration (e.g., O(T^{0.5}) regret of online mirror descent). On the other hand, conditional gradient variants solve a linear optimization in each iteration, but result in suboptimal rates (e.g., OT^{0.75}) regret of online FrankWolfe). Motivated by this tradeoff in runtime v/s convergence rates, we consider iterative projections of closeby points over widelyprevalent submodular base polytopes B(f). We develop a toolkit to speed up the computation of projections using both discrete and continuous perspectives. We subsequently adapt the awaystep FrankWolfe algorithm to use this information and enable early termination.

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTClique Trees and Disjunctive Constraints11th Floor Lecture Hall
 Speaker
 Illya Hicks, Rice University
 Session Chair
 Karthekeyan Chandrasekaran, University of Illinois UrbanaChampaign
Abstract
In this talk, we explore the concept of combinatorial disjunctive constraints (CDC) and their properties. In particular, we examine when one can build small ideal mixedinteger programming (MIP) formulations using CDCs and their linkages to clique trees. We also show that generalized special ordered sets (SOS k) can be modeled by CDCs with ties to clique trees.

11:30 am  12:15 pm EDTLower Bounds on the Complexity of MixedInteger Programs for Stable Set and Knapsack11th Floor Lecture Hall
 Speaker
 Stefan Weltge, Technical University of Munich
 Session Chair
 Karthekeyan Chandrasekaran, University of Illinois UrbanaChampaign
Abstract
Standard mixedinteger programming formulations for the stable set problem on nnode graphs require n integer variables. We prove that this is almost optimal: We give an explicit family of stable set polytopes of nnode graphs for which every polynomialsize formulation requires Ω(n / log^2 n) integer variables. By a polyhedral reduction we obtain an analogous result for nitem knapsack polytopes. This improves the previously known bounds of Ω(√n / log n) by Cevallos, Weltge & Zenklusen (SODA 2018). To this end, we extend a result of Göös, Jain & Watson (FOCS 2016, SIAM J. Comput. 2018) showing that the linear extension complexity of stable set polytopes of some nnode graphs is 2^(Ω(n / log n)). We show that the same bound holds for ɛ/napproximations of these polytopes, for some constant ɛ > 0. On this way, we simplify several of their original arguments to obtain a proof that is accessible to a broader community. For instance, our proof does not require reductions to certain CSP problems or the notion of KarchmerWigderson games. This is joint work with Jamico Schade and Makrand Sinha.

12:30  2:00 pm EDTNetworking LunchLunch/Free Time  11th Floor Collaborative Space

2:00  2:45 pm EDTArc connectivity and submodular flows in digraphs11th Floor Lecture Hall
 Speaker
 Ahmad Abdi, London School of Economics
 Session Chair
 Steffen Borgwardt, University of Colorado Denver
Abstract
Given a digraph D, and an integer k>=1, a karcconnected flip is an arc subset whose reversal makes the digraph (strongly) karcconnected. The main result of this work introduces a sufficient condition for the existence of a karcconnected flip that is also a submodular flow for a crossing submodular function. The main result has several applications to graph orientations and combinatorial optimization. For instance, if the underlying graph of D is tedgeconnected for some integer t>=2, there exists a decomposition of the arc set into a karcconnected flip and a (tk)dijoin, for any integer k such that 1<=k<=t/2. This extends NashWilliams’ weak orientation theorem, as well as proves a weaker variant of Woodall’s conjecture on such digraphs. The main result follows from a surprising sufficient condition for the existence of capacitated integral solutions to the intersection of two submodular flow systems. This result in turn has some applications for submodular optimization. For instance, in a weakly connected digraph, the intersection of two submodular flow systems defines an integral polyhedron. Joint work with Gerard Cornuejols and Giacomo Zambelli.

3:00  3:45 pm EDTSmoothed Analysis of the Simplex Method11th Floor Lecture Hall
 Speaker
 Sophie Huiberts, Columbia University
 Session Chair
 Steffen Borgwardt, University of Colorado Denver
Abstract
Explaining why the simplex method is fast in practice, despite it taking exponential time in the theoretical worst case, continues to be a challenge. Smoothed analysis is a paradigm for addressing this question. During my talk I will present recent progress in the smoothed complexity of the simplex method, discussing both upper and lower bounds.

4:00  4:30 pm EDTCoffee Break11th Floor Collaborative Space

4:30  6:00 pm EDT
Wednesday, March 29, 2023

9:00  9:45 am EDTDegree Sequence Optimization and Sparse Integer Programming11th Floor Lecture Hall
 Speaker
 Shmuel Onn, Technion  Israel Institute of Technology
 Session Chair
 Antoine Deza, McMaster University
Abstract
I will suggest several open problems on optimization over degree sequences of graphs and hypergraphs and over line sums of matrices; describe several recent partial results such as for convex functions, complete graphs, complete bipartite graphs and monotone matrices, and bounded tree width or depth; and outline some proof techniques, including our recent powerful theory of sparse integer programming in high dimensions, which will be explained.

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTAlgorithmic, combinatorial, and geometric aspects of linear optimization11th Floor Lecture Hall
 Speaker
 Lionel Pournin, University of Paris 13
 Session Chair
 Antoine Deza, McMaster University
Abstract
The simplex and interior point methods are currently the most computationally successful algorithms for linear optimization. While simplex methods follow an edge path, interior point methods follow the central path. The complexity of these methods is closely related to the combinatorial and geometric structures of the feasible region. Focusing on the analysis of worstcase constructions leading to computationally challenging instances, recently obtained lower bounds on the largest possible diameter of lattice polytopes will be presented. These bounds, via lattice zonotopes, are established using tools from combinatorics and number theory. This talk is based on joint work with Antoine Deza.

11:30 am  12:15 pm EDTThe Exact Bipartite Matching Polytope Has Exponential Extension Complexity11th Floor Lecture Hall
 Speaker
 Ola Svensson, EPFL
 Session Chair
 Antoine Deza, McMaster University
Abstract
Given a graph with edges colored red or blue and an integer k, the exact perfect matching problem asks if there exists a perfect matching with exactly k red edges. There exists a randomized polylogarithmictime parallel algorithm to solve this problem, dating back to the eighties, but no deterministic polynomialtime algorithm is known, even for bipartite graphs. In this talk, we discuss known approaches and their limitations. In particular, we show that there is no subexponentialsized linear program that can describe the convex hull of exact matchings in bipartite graphs. In fact, we prove something stronger, that there is no subexponentialsized linear program to describe the convex hull of perfect matchings with an odd number of red edges. To prove our result, we devise an exponential set of valid constraints that we believe are interesting in their own right. In particular, we leave as an open problem whether they define the convex hull of perfect matchings with an odd number of red edges.
This is joint work with Xinrui Jia and Weiqiang Yuan 
12:15  12:30 pm EDTGroup Photo (Immediately After Talk)11th Floor Lecture Hall

12:30  2:30 pm EDTLunch/Free Time

2:30  3:15 pm EDTApproximating Weighted Connectivity Augmentation Below Factor 211th Floor Lecture Hall
 Speaker
 Rico Zenklusen, ETH Zurich
 Session Chair
 Sophie Huiberts, Columbia University
Abstract
The Weighted Connectivity Augmentation Problem (WCAP) asks to augment the edgeconnectivity of a graph by adding a min cost edge set among given candidate edges. It is among the most elementary network design problems for which no betterthan2 approximation has been known, whereas 2approximations can easily be obtained through a variety of wellknown techniques. In this talk, I will discuss an approach showing that approximation factors below 2 are achievable for WCAP, ultimately leading to a (1.5+epsilon)approximation. Our approach is based on a highly structured directed simplification of WCAP with planar optimal solutions. We show how one can successively improve solutions of this directed simplification by moving to mixed solutions, consisting of both directed and undirected edges. These insights can be leveraged in local search and relative greedy strategies, inspired by recent advances on the Weighted Tree Augmentation Problem, to obtain a (1.5+epsilon)approximation. This is joint work with Vera Traub.

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTUnit and distinct distances in typical norms11th Floor Lecture Hall
 Speaker
 Lisa Sauermann, MIT
 Session Chair
 Sophie Huiberts, Columbia University
Abstract
Given n points in the plane, how many pairs among these points can have distance exactly 1? More formally, what is the maximum possible number of unit distances among a set of n points in the plane? This problem is a very famous and still largely open problem, called the Erdos unit distance problem. One can also study this problem for other norms on R^2 (or more generally on R^d for any dimension d) that are different from the Euclidean norm. This direction has been suggested in the 1980s by Ulam and Erdos and attracted a lot of attention over the years. We give an almost tight answer to this question for almost all norms on R^d (for any given d). Furthermore, for almost all norms on R^d, we prove an asymptotically tight bound for a related problem, the socalled Erdos distinct distances problem. Our proofs rely in part on arguments from polyhedral geometry (and some tools from matroid theory are also relevant). Joint work with Noga Alon and Matija Bucic.
Thursday, March 30, 2023

9:00  9:45 am EDTUnderstanding graphs locally11th Floor Lecture Hall
 Speaker
 Annie Raymond, University of Massachusetts, Amherst
 Session Chair
 Mohit Singh, Georgia Tech
Abstract
Graphs are ubiquitous in modern applicationsincluding some very large graphs. This leads one to wonder, "How can we understand such large graphs?" One prevalent idea is to observe them locally: to count how many times certain substructures appear. If one knows something about the number of some particular substructures in a graph, what can one say about the number of other substructures or about global properties of the graph in general? Such problems are at the heart of extremal graph theory. In this talk, we will discuss successes and challenges in proving inequalities involving these substructures. We will also encounter graph profiles, complicated objects that allow us to understand all polynomial inequalities involving some fixed set of substructures. This is joint work with Greg Blekherman, Mohit Singh, Rekha Thomas and Fan Wei.

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTUntangling near minimum cuts with applications in network design11th Floor Lecture Hall
 Speaker
 Nathan Klein, University of Washington
 Session Chair
 Mohit Singh, Georgia Tech
Abstract
The structure of the set of global minimum cuts of a graph is well understood and is captured by a cactus, as proved by Dinitz, Karzanov, and Lomonosov in the 70s. However, even for small epsilon, the set of (1+epsilon) near minimum cuts has a significantly more complex structure. Benczúr and Goemans studied near minimum cuts starting in the late 90s and showed that they admit a socalled polygon representation. In this talk I will show new algorithmically useful properties of this representation and demonstrate two applications in approximating network design problems.

11:30 am  12:15 pm EDTThe Subspace Flatness Conjecture and Faster Integer Programming11th Floor Lecture Hall
 Speaker
 Thomas Rothvoss, University of Washington
 Session Chair
 Mohit Singh, Georgia Tech
Abstract
In a seminal paper, Kannan and Lov\'asz (1988) considered a quantity $\mu_{KL}(\Lambda,K)$ which denotes the best volumebased lower bound on the covering radius $\mu(\Lambda,K)$ of a convex body $K$ with respect to a lattice $\Lambda$. Kannan and Lov\'asz proved that $\mu(\Lambda,K) \leq n \cdot \mu_{KL}(\Lambda,K)$ and the Subspace Flatness Conjecture by Dadush (2012) claims a $O(\log n)$ factor suffices, which would match the lower bound from the work of Kannan and Lov\'asz. We settle this conjecture up to a constant in the exponent by proving that $\mu(\Lambda,K) \leq O(\log^{7}(n)) \cdot \mu_{KL} (\Lambda,K)$. Our proof is based on the Reverse Minkowski Theorem due to Regev and StephensDavidowitz (2017). Following the work of Dadush (2012, 2019), we obtain a $(\log n)^{O(n)}$time randomized algorithm to solve integer programs in $n$ variables. Another implication of our main result is a nearoptimal flatness constant of $O(n \log^{8}(n))$. This is joint work with Victor Reis.

12:30  2:30 pm EDTNetworking LunchLunch/Free Time  11th Floor Collaborative Space

2:30  3:15 pm EDTTransshipments over time, submodular functions, and discrete Newton11th Floor Lecture Hall
 Speaker
 Martin Skutella, TU Berlin
 Session Chair
 Annie Raymond, University of Massachusetts, Amherst
Abstract
The Quickest Transshipment Problem is to route flow as quickly as possible from sources with supplies to sinks with demands in a network with capacities and transit times on the arcs. It is of fundamental importance for numerous applications in areas such as logistics, traffic, evacuation, and finance. More than 25 years ago, Hoppe and Tardos presented the first (strongly) polynomialtime algorithm for this problem. Their approach, as well as subsequently derived algorithms with strongly polynomial running time, is hardly practical as it relies on parametric submodular function minimization via Megiddo's parametric search. We present considerably faster algorithms for the Quickest Transshipment Problem that instead employ a subtle extension of the Discrete Newton Method. This improves the previously best known running time of $\tilde{O}(m^4k^{14})$ to $\tilde O(m^2k^5+m^3k^3+m^3n)$, where $n$ is the number of nodes, $m$ the number of arcs, and $k$ the number of source and sink nodes. Furthermore, we show how to compute integral quickest transshipments in $\tilde O(m^2k^6+m^3k^4+m^3n)$ time.
This is joint work with Miriam Schlöter and Khai Van Tran. 
3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTOpenly Disjoint Paths, Jump Systems, and Discrete Convexity11th Floor Lecture Hall
 Speaker
 Satoru Iwata, University of Tokyo
 Session Chair
 Annie Raymond, University of Massachusetts, Amherst
Abstract
In 1978, Mader discovered a minmax theorem on the number of openly disjoint paths between terminals. Sadli and Sebo (2000) showed that the set of integer vectors in that appear as degree sequences of openly disjoint paths forms a jump system. In this talk, we describe an alternative proof of this fact by using a reduction to matroid matching, which was originally observed by Lovasz (1980). In addition, we show that a function on this jump system determined by the minimum total length of openly disjoint paths enjoys the Mconvexity introduced by Murota (2006).
Friday, March 31, 2023

9:00  9:45 am EDTThin trees for laminar families11th Floor Lecture Hall
 Speaker
 Neil Olver, London School of Economics
 Session Chair
 Britta Peis, RWTH Aachen University
Abstract
In the strong form of the thin tree conjecture, formulated by Goddyn in 2004, we are given a kedgeconnected graph and wish to find a tree containing at most an O(1/k) fraction of the edges across every cut. This conjecture, if true, has a variety of implications in a number of areas such as graph theory and approximation algorithms. A natural relaxation of this problem is to find a tree with at most O(1/k) edges across a fixed collection of cuts, instead of all cuts. Via a simple reduction technique followed by iterative relaxation, we show that the thin tree conjecture is true for laminar families of cuts, resolving an open question of Olver and Zenklusen from 2013. Joint work with Nathan Klein.

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTStreaming algorithms for ksubmodular maximization and ad allocation11th Floor Lecture Hall
 Speaker
 Alina Ene, Boston University
 Session Chair
 Britta Peis, RWTH Aachen University
Abstract
Maximizing a monotone ksubmodular function subject to cardinality constraints is a general model for several applications ranging from influence maximization with multiple products to sensor placement with multiple sensor types and online ad allocation. Due to the large problem scale in many applications and the online nature of ad allocation, a need arises for algorithms that process elements in a streaming fashion and possibly make online decisions. In this talk, we present a streaming algorithm for maximizing a monotone ksubmodular function subject to a percoordinate cardinality constraint attaining an approximation guarantee close to the state of the art guarantee in the offline setting. We also give a variant of the algorithm that is able to leverage machine learning predictions.

11:30 am  12:15 pm EDTNonAdaptive Matroid Prophet Inequalities11th Floor Lecture Hall
 Speaker
 Kanstantsin Pashkovich, University of Waterloo
 Session Chair
 Britta Peis, RWTH Aachen University
Abstract
We consider the matroid prophet inequality problem. This problem has been extensively studied in the case of adaptive mechanisms. In particular, there is a tight 2competitive mechanism for all matroids. However, it is not known what classes of matroids admit nonadaptive mechanisms with constant guarantee. Recently, it was shown that there are constantcompetitive nonadaptive mechanisms for graphic matroids. In this talk, we show that various known classes of matroids admit constantcompetitive nonadaptive mechanisms.

12:30  2:30 pm EDTLunch/Free Time

2:30  3:15 pm EDTApproximating Nash Social Welfare for Submodular Valuations11th Floor Lecture Hall
 Speaker
 László Végh, London School of Economics
 Session Chair
 Gerard Cornuejols, Carnegie Mellon University
Abstract
The Nash social welfare (NSW) problem asks for an allocation of indivisible items to agents in order to maximize the geometric mean of agents’ valuations. This is a common objective for fair division, representing a balanced tradeoff between the often conflicting requirements of fairness and efficiency. The problem is NPcomplete already for additive valuation functions. We present a simple, deterministic 4approximation algorithm for the Nash Social Welfare problem under the general class submodular valuation functions. The previous best approximation factor was 380 via a randomized algorithm. We also consider the asymmetric variant of the problem where the objective is to maximize the weighted geometric mean of agents’ valuations, and give a (α+2)eapproximation, where α is the ratio between largest weight and the average weight. This is joint work with Jugal Garg, Edin Husić, Wenzheng Li, and Jan Vondrák.

3:30  4:15 pm EDTOptimal Deployment of Electric Vehicle Charging Infrastructure via Bilevel Optimization11th Floor Lecture Hall
 Speaker
 Miguel Anjos, University of Edinburgh
 Session Chair
 Gerard Cornuejols, Carnegie Mellon University
Abstract
The increase of electric vehicle (EV) adoption in recent years has correspondingly increased the importance of providing adequate charging infrastructure for EV users. For a charging service provider, the fundamental question is to determine the optimal location and sizing of charging stations with respect to a given objective and subject to budget and other practical constraints. One possible objective is to maximize EV adoption as part of a public policy on electric transportation. Alternatively, the objective may be to maximize the profit gained from providing this service, in which case the price of charging is also to be optimized. These problems are fundamentally combinatorial and frequently formulated using mixedinteger linear optimization. In this talk, the focus will be on the use of bilevel optimization in this area, in particular to more accurately capture the interactions between the charging service provider and the EV users.

4:30  5:00 pm EDTCoffee Break11th Floor Collaborative Space
Monday, April 3, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, April 4, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

9:00  10:00 am EDTProfessional Development: Papers and JournalsProfessional Development  11th Floor Lecture Hall

10:30  11:15 am EDTGenerating Short Monotone Paths in 0/1 LPsSeminar  11th Floor Lecture Hall
 Sean Kafer, University of Waterloo
Abstract
Even after decades of study, it is unknown whether there exists a pivot rule for the Simplex method that always solves an LP with only a polynomial number of pivots. This remains unknown even in the special case of 0/1 LPs  those defined over polytopes whose vertices are in $\{0,1\}^n$  a case that includes many extensively studied problems in combinatorial optimization. In the pursuit of better understanding the behavior of the Simplex method on 0/1 LPs, we study the length of the monotone path generated by following steepest edges, where here we determine steepness by normalizing with the 1norm instead of the usual 2norm. We show that this path is of a stronglypolynomial length and that it can be computed in polynomial time. We achieve this by first considering the length of the socalled circuitpath generated by steepest descent circuit steps, where the circuits are a set of augmentation directions that generalize the set of edges. We then show that, at an extreme point solution of a 0/1 LP, a steepest descent circuit step is always equal to a steepest descent edge step, i.e., that these concepts are unified in the setting of 0/1 LPs. In light of the fact that these results do not describe the behavior of the steepest edge Simplex pivot rule, we devise an alternate pivot rule for 0/1 LPs which is guaranteed to follow the path generated by steepest edges. That is, we show the existence of a Simplex pivot rule for 0/1 LPs which is guaranteed to require only a stronglypolynomial number of nondegenerate pivots. We build upon this by giving two additional Simplex pivot rules for 0/1 LPs  instead inspired by the classical Shadow Vertex pivot rule  whose number of nondegenerate pivots are, respectively, at most the number of variables and at most the the dimension of the feasible region, achieving optimal diameter bounds for the class of 0/1 polytopes. Joint work with JesUs De Loera, Laura Sanita, and Alex Black.

11:15 am  12:00 pm EDTDyadic Linear ProgrammingSeminar  11th Floor Lecture Hall
 Virtual Speaker
 Gerard Cornuejols, Carnegie Mellon University
Abstract
A finite vector is dyadic if each of its entries is a dyadic rational number, i.e. if it has an exact floating point representation. In joint work with Ahmad Abdi, Bertrand Guenin, and Levent Tuncel, we study the problem of finding a dyadic optimal solution to a linear program, if one exists.

12:15  12:30 pm EDTOrganizer Group PhotoGroup Photo (Immediately After Talk)  11th Floor Lecture Hall

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, April 5, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, April 6, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

2:00  2:30 pm EDTCompetitive Equilibrium and Lattice PolytopesPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
 MarieCharlotte Brandenburg, Max Planck Institute for Mathematics in the Sciences
Abstract
The question of existence of a competitive equilibrium is a game theoretic question in economics. It can be posed as follows: In a given auction, can we make an offer to all bidders, such that no bidder has an incentive to decline our offer? We consider a mathematical model of this question in which the auction is modeled via weights on a simple graph. In this model, the existence of an equilibrium can be translated to a condition on certain lattice points in a lattice polytope. In this talk, we discuss this translation to the polyhedral language. Using polyhedral methods, we show that in the case of the complete graph a competitive equilibrium is indeed guaranteed to exist. Along the way, we are going to meet the correlation polytope (aka the boolean quadric polytope), which is a sibling of the even more famous cutpolytope, and we make use of an LPrelaxation of this polytope due to Padberg (1989) to obtain this result. This talk is based on joint work with Christian Haase and Ngoc Mai Tran.

2:30  3:00 pm EDTReLU Neural Networks of Polynomial Size for Exact Maximum Flow ComputationPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
 Christoph Hertrich, The London School of Economics and Political Science
Abstract
Neural networks with rectified linear unit (ReLU) activations are one of the most popular modern machine learning models. A function can be computed by a ReLU network (of arbitrary size) if and only if it is continuous and piecewise linear. We pose the following fundamental question: Which functions can be computed by a ReLU network of polynomial size? In order to study this question, we propose to view ReLU networks as a model of (realvalued) computation and investigate the complexity of different problems in this model. Specifically, we show that there exist polynomialsize ReLU networks to compute (i) the value of a minimum spanning tree from given edge weights in a graph, and (ii) a maximum stflow from given arc capacities in a flow network. These results imply in particular that the respective problems can be solved with strongly polynomial time algorithms that solely use affine transformations and maxima computations, but no conditional branchings. This is joint work with Leon Sering (ETH Zürich).

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Friday, April 7, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Monday, April 10, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, April 11, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

9:00  10:00 am EDTProfessional Development: Job ApplicationsProfessional Development  11th Floor Lecture Hall

10:30  11:15 am EDTAggregations of quadratic inequalities and hyperplane hidden convexitySeminar  11th Floor Lecture Hall
 Santanu Dey, Georgia Institute of Technology.
Abstract
We study properties of the convex hull of a set S described by quadratic inequalities. A simple way of generating inequalities valid on S is to take a nonnegative linear combinations of the defining inequalities of S. We call such inequalities aggregations. Special aggregations naturally contain the convex hull of S, and we give sufficient conditions for such aggregations to define the convex hull. We introduce the notion of hidden hyperplane convexity (HHC), which is related to the classical notion of hidden convexity of quadratic maps. We show that if the quadratic map associated with S satisfies HHC, then the convex hull of S is defined by special aggregations. To the best of our knowledge, this result generalizes all known results regarding aggregations defining convex hulls. Using this sufficient condition, we are able to recognize previously unknown classes of sets where aggregations lead to convex hull. We show that the condition known as positive definite linear combination together with hidden hyerplane convexity is a sufficient condition for finitely many aggregations to define the convex hull. All the above results are for sets defined using open quadratic inequalities. For closed quadratic inequalities, we prove a new result regarding aggregations giving the convex hull, without topological assumptions on S. This is joint work with Grigoriy Blekherman and Shengding Sun.

11:15 am  12:00 pm EDTAdmissibility of solution estimators in stochastic optimizationSeminar  11th Floor Lecture Hall
 Amitabh Basu, Johns Hopkins University
Abstract
We look at stochastic optimization problems through the lens of statistical decision theory. In particular, we address admissibility, in the statistical decision theory sense, of the natural sample average estimator for a stochastic optimization problem (which is also known as the empirical risk minimization (ERM) rule in learning literature). It is well known that for some simple stochastic optimization problems, the sample average estimator may not be admissible. This is known as Stein's paradox in the statistics literature. We show that for optimizing stochastic linear functions over compact sets, the sample average estimator is admissible. Moreover, we study problems with convex quadratic objectives subject to box constraints. Stein's paradox holds when there are no constraints and the dimension of the problem is at least three. We show that in the presence of box constraints, admissibility is recovered for dimensions 3 and 4.

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, April 12, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, April 13, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Friday, April 14, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Monday, April 17, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, April 18, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

9:00  10:00 am EDTProfessional Development: Grant ProposalsProfessional Development  11th Floor Lecture Hall

10:30  11:15 am EDTCyclic polytopes, curves, and volumesSeminar  11th Floor Lecture Hall
 Chiara Meroni, ICERM
Abstract
How can one compute the volume of the convex hull of a curve? I will try to answer this question, for special families of curves. This generalizes a previously known integral formula. Our methods involve approximating the curve with cyclic polytopes and using the tool of "path signature". I will give a geometric interpretation of this volume formula in terms of lengths and areas, and conclude with examples and an open conjecture. This is a joint work with Carlos Améndola and Darrick Lee.

11:15 am  12:00 pm EDTKissing lattice polytopesSeminar  11th Floor Lecture Hall
 Antoine Deza, McMaster University
Abstract
Motivated by algorithmic applications we consider the smallest possible distance between two disjoint lattice polytopes in dimension d. Assuming that the polytopes are described as a convex hull of vertices whose coordinates are drawn from {0,1,….,k}, we show that, for d large enough, the distance between two disjoint lattice polytopes is at least 1 over (dk)^{2d} and exhibit polytopes at distance 1 over (k root(d))^root(d). Joint work with Shmuel Onn, Sebastian Pokutta, and Lionel Pournin.

12:00  12:05 pm EDTSemester Program Group PhotoGroup Photo (Immediately After Talk)  11th Floor Lecture Hall

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, April 19, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, April 20, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

2:00  2:30 pm EDTOn fast algorithms for fundamental problems in combinatorial optimizationPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
 Bento Natura, Georgia Tech
Abstract
Over the past year, there have been tremendous developments in highaccuracy solvers for fundamental problems in combinatorial optimization and operational research, such as shortest path and minimumcost flow. Notably, while some of these techniques rely on continuous optimization methods, the current fastest algorithm for shortest paths is purely combinatorial. In this talk, we will explore the key concepts of this algorithm and provide a general overview of recent advancements in this field.

2:30  3:00 pm EDTMonotone Path PolytopesPost Doc/Graduate Student Seminar  11th Floor Lecture Hall
 Alex Black, UC Davis
Abstract
Understanding the worstcase runtime of the simplex method remains as one of the most fundamental open problems in the theory of linear programming. One of the primary challenges for this problem is that we don't know how to find short paths on polytopes that improve a linear objective function at each step, called monotone paths. However, in this talk, I will discuss how monotone paths on polytopes relate to geometric combinatorics. In particular, I will introduce the monotone path polytope construction from the theory of fiber polytopes by Billera and Sturmfels and discuss some of the remarkable combinatorics and open problems that arise from studying examples of monotone path polytopes.

3:00  3:15 pm EDTPostdoc / Graduate Student PhotoGroup Photo (Immediately After Talk)  11th Floor Collaborative Space

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Friday, April 21, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Monday, April 24, 2023

8:30  8:50 am EDTCheck In11th Floor Collaborative Space

8:50  9:00 am EDTWelcome11th Floor Lecture Hall
 Brendan Hassett, ICERM/Brown University

9:00  9:45 am EDTSolving MixedInteger Semidefinite Programs11th Floor Lecture Hall
 Speaker
 Marc Pfetsch, TU Darmstadt
 Session Chair
 Santanu Dey, Georgia Institute of Technology.
Abstract
Mixedinteger semidefinite programs form an interesting generalization of mixedinteger linear programs with many applications. Here, some of the variables of a semidefinite program are required to be integer. This talk will introduce new methods as well as techniques that can be generalized from the linear to the semidefinite world. This includes presolving methods, e.g., fixing of variables, bound strengthening etc. Moreover, handling of symmetries and conflict analysis can be adapted and have a positive impact on the performance. The talk will also try to highlight the differences between the linear and semidefinite setting. The impact of the methods will be illustrated computationally, using SCIPSDP, an opensource solver for mixedinteger semidefinite programs based on SCIP.

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTMeasuring the Importance of Facets of Cyclic Group Polyhedra Using Solid Angles11th Floor Lecture Hall
 Speaker
 Yuan Zhou, University of Kentucky
 Session Chair
 Santanu Dey, Georgia Institute of Technology.
Abstract
Solid angle of a polyhedral cone, which indicates the proportion of space occupied by the cone, is of significant interest in discrete optimization. Gomory introduced the cyclic group relaxation of IP. The facets of the cyclic group polyhedra are useful in generating cutting planes. To predict the importance or relative size of each facet, researchers have used the shooting experiment, which provides an estimate of the solid angle subtended by the facet at the origin. However, the obtained sizes were not always consistent due to randomness. We propose to use the solid angles measure, whose closed formulas were well established in two and three dimensions. For higher dimensions, Aomoto and Ribando showed that the solid angle of a simplicial cone can be computed using a multivariable hypergeometric series, provided that the cone satisfies a certain condition related to positivedefiniteness. We provide decomposition methods to ensure that the positivedefinite criterion is met. We present our results of the solid angle measures and compare them with those obtained from the shooting experiments.

11:30 am  12:15 pm EDTSafe and verified cutting planes in an exact MIP framework11th Floor Lecture Hall
 Speaker
 Ambros Gleixner, HTW & Zuse Institute Berlin
 Session Chair
 Santanu Dey, Georgia Institute of Technology.
Abstract
The presence of floatingpoint roundoff errors compromises the results of virtually all fast mixedinteger programming solvers available today. In this talk we present recent advances in our endeavour to craft a performant mixedinteger optimizer that is not only free from roundoff errors, but also produces certificates of optimality that can be verified independently of the solving process. We provide an overview of the entire framework, which is an extension of the open solver SCIP. We focus in particular on the safe generation and verification of Gomory mixedinteger cuts via mixedinteger rounding. This is joint work with Sander Borst, Leon Eifler, Fabian Frickenstein, and Jules NicolasThouvenin.

12:30  2:30 pm EDTLunch/Free Time

2:30  3:15 pm EDTLinear lexicographic optimization and preferential bidding system11th Floor Lecture Hall
 Speaker
 Frédéric Meunier, École Nationale des Ponts et Chaussées, CERMICS
 Session Chair
 Amitabh Basu, Johns Hopkins University
Abstract
Some airlines use the preferential bidding system to construct the schedules of their pilots. In this system, the pilots bid on the different activities and the schedules that lexicographically maximize the scores of the pilots according to their seniority are selected. A sequential approach to solve this maximization problem is natural: the problem is first solved with the bids of the most senior pilot; then it is solved with those of the second most senior without decreasing the score of the most senior, and so on. The literature admits that the structure of the problem somehow imposes such an approach. The problem can be modeled as an integer linear lexicographic program. We propose a new exact method, which relies on column generation for solving its continuous relaxation. To design this column generation, we prove that bounded linear lexicographic programs admit “primaldual” feasible bases and we show how to compute such bases efficiently. Another contribution on which our exact method relies consists in the extension of standard tools for resourceconstrained longest path problems to their lexicographic versions. Numerical experiments show that this new method is already able to solve industrial instances provided by Air France, with up to 150 pilots. Joint work with Nour ElHouda Tellache and Axel Parmentier

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTMathematical Optimization for Traffic Management in Urban Air Mobility11th Floor Lecture Hall
 Speaker
 Claudia D'Ambrosio, LIX  Ecole Polytechnique
 Session Chair
 Amitabh Basu, Johns Hopkins University
Abstract
We focus on how mathematical optimization (MO) could help build the bricks to develop Urban Air Mobility (UAM). In particular, we focus on passengers’ transportation via eVTOLs, i.e., electric flying vehicles that will allow exploiting the sky to help smooth ground traffic in densely populated areas. Clearly, one of the biggest challenges in UAM is to ensure safety. From an operational viewpoint, the flights planning can be highly affected by different kinds of disruptions, which have to be solved at the tactical deconfliction level. Inspired by the classical aircraft deconfliction, we propose a MO formulation based on a mathematical definition of vehicles separation, specialized in the UAM context. The deconfliction is based on speed changes or delayed takeoff, when possible. To the best of our knowledge, our MO model is the first that considers the whole set of conflicts at the same time. In the computational study, we, thus, compare our approach against a variant considering only pairwise conflicts, on three sets of realistic scenarios. More details can be found in Pelegrin et. al (2021).

5:00  6:30 pm EDTReception11th Floor Collaborative Space
Tuesday, April 25, 2023

9:00  9:45 am EDTA NASA Perspective on Quantum Computing, with Emphasis on Recent Results in Distributed Computing11th Floor Lecture Hall
 Speaker
 Eleanor Rieffel, NASA
 Session Chair
 Giacomo Nannicini, University of Southern California
Abstract
The NASA Quantum Artificial Intelligence Laboratory (QuAIL) performs research to assess the potential impact of quantum computers on challenging computational problems relevant to NASA missions of the future, with particular emphasis on discrete optimization. The talk will begin with a brief overview of the QuAIL team and some general remarks on the status of and prospects for quantum computing. The talk will then transition to a discussion of distributed quantum computing, with an emphasis on recent results in the quantum CONGESTCLIQUE Model (qCCM). I’ll introduce both the classical and quantum CONGESTCLIQUE Models of distributed computation, and then outline two quantum algorithms that succeed with high probability; one yields an approximately optimal Steiner Tree, and the other an exact directed minimum spanning tree, each using asymptotically fewer rounds of communication than any known algorithms in the classical CONGESTCLIQUE model. We achieve these results by combining classical algorithms with fast quantum subroutines. Additionally, we characterize the constants and logarithmic factors involved in our algorithms, as well as related prior classical and quantum algorithms, revealing the importance of “small” factors and highlighting that advances are needed to render both practical. The talk will conclude with some open questions.

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTCompiled nonlocal games: sumofsquares optimization meets cryptography?11th Floor Lecture Hall
 Speaker
 Anand Natarajan, MIT
 Session Chair
 Giacomo Nannicini, University of Southern California
Abstract
Nonlocal games are a fundamental tool for testing quantum systems, but their power depends on spatial separation: a verifier must be able to separately interact with two quantum systems that cannot communicate with each other. In 2022, Kalai, Lombardi, Vaikuntanathan, and Yang proposed a method to "compile" any nonlocal game into an interaction with a *single* quantum device, using cryptography to simulate spatial separation. However, they could not characterize the behavior of quantum devices in their protocols (only classical devices). In this work, we make progress on this question by showing that the compiled version of the CHSH game forces the device to use two anticommuting observables, just as the nonlocal version does, and as a consequence obtain an efficient argument system for polynomialtime quantum computations. Our proof is based on a modification of the noncommutative sumofsquares method, which is one of the few general techniques known to analyze nonlocal games. Joint work with Tina Zhang, MIT.

11:30 am  12:15 pm EDTApproximation and Hardness Results for Quantum Max Cut11th Floor Lecture Hall
 Speaker
 Ojas Parekh, Sandia National Laboratories
 Session Chair
 Giacomo Nannicini, University of Southern California
Abstract
We will explore synergies between classical discrete optimization problems and the Local Hamiltonian problem, a natural quantum generalization of classical constraint satisfaction problems (CSPs). We will consider Quantum Max Cut, a QMAhard 2Local Hamiltonian problem. Quantum Max Cut is emerging as a testbed for approximating 2Local Hamiltonian problems analogously to Max Cut’s role as a canonical CSP and discrete optimization problem that has driven development of classical heuristics, approximation algorithms, and hardness results. We will discuss several recent results including an optimal productstate approximation for Quantum Max Cut based on a quantum version of the Lasserre hierarchy, as well as prospects for UniqueGames hardness. This talk is aimed at a broad audience and assumes no background in quantum physics.

12:30  2:30 pm EDTNetworking LunchLunch/Free Time  11th Floor Collaborative Space

2:30  3:15 pm EDTQuantum Annealing and Combinatorial Optimization11th Floor Lecture Hall
 Speaker
 Carleton Coffrin, Los Alamos National Laboratory
 Session Chair
 Swati Gupta, Georgia Tech
Abstract
Over the past decade the usefulness of quantum computing hardware for combinatorial optimization has been the subject of much debate. One of the central challenges of this discussion is that theoretical analysis thus far only predicts a quadratic improvement in computational complexity for quantumaccelerated optimization algorithms. In this regime runtime performance benchmarking plays an important role in understanding and quantifying the potential benefits of quantum computing for optimization tasks. In this work, we will review the mathematical foundations of the Quantum Annealing algorithm for combinatorial optimization and conduct a performance assessment of DWave Systems' most recent “Advantage Performance Update” computer. We show that classes of contrived problems exist where this quantum annealer can provide run time benefits over a collection of established solution methods. Although this work does not present strong evidence of an irrefutable performance benefit for this emerging quantum optimization technology, it does exhibit encouraging progress, signaling potential impacts on practical optimization tasks in the future.

3:30  4:00 pm EDTPoster Session BlitzLightning Talks  11th Floor Collaborative Space
 Speakers
 Rachael Alfant, Rice University
 Cristina MoleroRío, École Polytechnique
 Renan Spencer Trindade, École Polytechnique, France
 Nagisa Sugishita, University of Edinburgh
 William Wesley, University of California Davis
 Session Chair
 Swati Gupta, Georgia Tech

4:00  5:00 pm EDT
Wednesday, April 26, 2023

9:00  9:45 am EDTMilestones on the Quantum Utility Highway11th Floor Lecture Hall
 Speaker
 Catherine McGeoch, DWave Systems Inc.
 Session Chair
 Swati Gupta, Georgia Tech
Abstract
We introduce Quantum Utility, an approach to quantum performance evaluation that aims to capture the user experience by considering overhead costs associated with the quantum computation. We define Milestones, which may be thought of as demonstrations of quantum utility in restricted contexts associated with subsets of overheads. We evaluate performance of a DWave Advantage system with respect to three Milestones, and discuss these results in the context of technological progress of annealing based QPUs.

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTFirstorder methods for LP11th Floor Lecture Hall
 Speaker
 Miles Lubin, Hudson River Trading
 Session Chair
 Juan Pablo Vielma, Google
Abstract
We present new approaches for solving linear programming problems based on firstorder methods and discuss some of the implications for computational discrete optimization. Among other advantages over simplex and barrier methods, these approaches have demonstrated scalability to very large instances (billions of variables) and have the potential to run on new hardware platforms. The talk covers recent theoretical and computational developments, including the release of PDLP in the ORTools library, and reviews preliminary applications in integer programming. This talk describes work completed while the speaker was at Google Research.

11:30 am  12:15 pm EDTNeural Network Verification As Piecewise Linear Optimization11th Floor Lecture Hall
 Speaker
 Joey Huchette, Google
 Session Chair
 Juan Pablo Vielma, Google
Abstract
In this talk we discuss how neural network verification (and related tasks) can be fruitfully modeled and solved using piecewise linear optimization techniques from operations research.

12:25  12:30 pm EDTGroup Photo (Immediately After Talk)11th Floor Lecture Hall

12:30  2:30 pm EDTLunch/Free Time

2:30  3:15 pm EDTMachine Learning for discrete optimization: Graph Neural Networks, generalization under shifts, and loss functions11th Floor Lecture Hall
 Speaker
 Stefanie Jegelka, MIT
 Session Chair
 Andrea Lodi, Cornell Tech
Abstract
Graph Neural Networks (GNNs) have become a popular tool for learning algorithmic tasks, in particular related to combinatorial optimization. In this talk, we will focus on the “algorithmic reasoning” task of learning a full algorithm. While GNNs have shown promising empirical results, their generalization properties are less well understood. We will try to understand in particular outofdistribution generalization in widely used message passing GNNs, with an eye on applications in learning for optimization: what may be an appropriate metric for measuring shift? Under what conditions will a GNN generalize to larger graphs? In the last part of the talk, we will take a brief look at objective (loss) functions for learning with discrete objects, beyond GNNs. In particular, neural networks work best with continuous, highdimensional spaces. Can we integrate this into appropriate loss functions?

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTUnderstanding Neural Network Expressivity via Polyhedral Geometry11th Floor Lecture Hall
 Speaker
 Christoph Hertrich, The London School of Economics and Political Science
 Session Chair
 Andrea Lodi, Cornell Tech
Abstract
Neural networks with rectified linear unit (ReLU) activations are one of the standard models in modern machine learning. Despite their practical importance, fundamental theoretical questions concerning ReLU networks remain open until today. For instance, what is the precise set of (piecewise linear) functions representable by ReLU networks with a given depth? Even the special case asking for the number of layers to compute a function as simple as max{0, x1, x2, x3, x4} has not been solved yet. In this talk we will explore the relevant background to understand this question and report about recent progress using polyhedral geometry as well as a computeraided approach based on mixedinteger programming.
Thursday, April 27, 2023

9:00  9:45 am EDTUsing Trained Machine Learning Predictors in Gurobi11th Floor Lecture Hall
 Speaker
 Tobias Achterberg, Gurobi Optimization
 Session Chair
 Volker Kaibel, OttovonGuericke Universität Magdeburg
Abstract
In this talk, we are interested in using machine learning predictors to model relationships between variables of a MIP optimization model in Gurobi. The inputs of the trained machine learning model are MIP decision variables, and the predicted output can be used in the objective function or in other constraints. In November 2022 we released the first version of the opensource ""gurobimachinelearning"" Python package on github.com. This package aims at making it easy to insert regression models trained by popular frameworks (e.g., scikitlearn, Keras, PyTorch) into a Gurobi model. The regression model may be a linear or logistic regression, a neural network, or based on decision trees. While the resulting optimization models have interesting potential applications, unfortunately they are often intractable with current technology. We present algorithmic improvements to Gurobi that improve performance on MIP models that include regression modelsin particular optimization models with embedded ReLU neural networks. Following Fischetti and Jo (2018), we apply optimization based bound tightening on the aggregated input variable of each neuron, processing neurons in layers from the input to the output layer. But since the MIP solver is unaware of the neural network structure, we first need to identify the layers of the network from the MIP formulation. This is done by a clustering algorithm, which is also discussed in this talk.

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTGlobal optimization with integers: modelbased and datadriven approaches11th Floor Lecture Hall
 Speaker
 Nick Sahinidis, Georgia Institute of Technology
 Session Chair
 Volker Kaibel, OttovonGuericke Universität Magdeburg
Abstract
We present recent methodological developments in the context of three closely related computational optimization projects: 1. The BARON project for algebraic optimization through a spatial branchandbound algorithm that exploits various convexification techniques. 2. The ALAMO project, which relies on algebraic global optimization (BARON) to build simple models from data while enforcing shape constraints. 3. The BAM project for datadriven optimization through the integration of sampling, partitioning, and global optimization (BARON) of local algebraic surrogates constructed from data (ALAMO). We discuss connections between the three projects, report on the status of each project and their integration, and present computations on established benchmarks and applications.

11:30 am  12:15 pm EDTConvex hull of a monomial on a twovariable conic domain11th Floor Lecture Hall
 Speaker
 Pietro Belotti, Politecnico di Milano
 Session Chair
 Volker Kaibel, OttovonGuericke Universität Magdeburg
Abstract
We consider a monomial function with real exponents, which is of interest in optimization. Specifically, global mixedinteger nonlinear optimization solvers need tight convex relaxations of sets defined by nonconvex functions to find a valid lower bound. The convex hull of the monomial in two variables on a bounding box is known for some special cases. We discuss the convex hull of a generic monomial in two variables restricted to a cone rather than a bounding box. We then look at how to compute the volume of such convex hull, which is also of interest in global optimization: branching operations of branchandbound solvers have a great impact in solver efficiency, in particular some branching techniques that aim at minimizing the total resulting volume of the two new subproblems.

12:30  2:30 pm EDTNetworking LunchLunch/Free Time  11th Floor Collaborative Space

2:30  3:15 pm EDTModeling and Duality in Domain Specific Languages for Mathematical Optimization11th Floor Lecture Hall
 Speaker
 Juan Pablo Vielma, Google
 Session Chair
 Marc Pfetsch, TU Darmstadt
Abstract
Domain specific languages (DSL) for mathematical optimization allow users to write problems in a natural algebraic format. In this talk we explore the design and implementation of ORTools’ MathOpt DSL.

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTSolving a family of mixed integer nonlinear programs with convex first order method roots11th Floor Lecture Hall
 Speaker
 Rahul Mazumder, Massachusetts Institute of Technology
 Session Chair
 Marc Pfetsch, TU Darmstadt
Abstract
We consider a family of convex integer programming problems arising in statistics/machine learning with sparsity structures. Unlike a line of work which relies on commercial MILP solvers, we design a specialized nonlinear branchandbound (BnB) framework, by critically exploiting the problem structure. An important component in our framework lies in efficiently solving the node relaxations using a specialized firstorder methods (e.g., coordinate descent). Our firstorder methods effectively leverage information across the BnB nodes through using warm starts, active sets, and screeningsome old, and some new tools developed in the context of largescale convex optimization.
Friday, April 28, 2023

9:00  9:45 am EDTContinuous cutting plane algorithms in integer programming11th Floor Lecture Hall
 Speaker
 Andrea Lodi, Cornell Tech
 Session Chair
 Tobias Achterberg, Gurobi Optimization
Abstract
Cutting planes for mixedinteger linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the socalled separation. Instead, we reframe the problem of finding good cutting planes as a continuous optimization problem over weights parametrizing families of valid inequalities. This problem can also be interpreted as optimizing a neural network to solve an optimization problem over subadditive functions, which we call the subadditive primal problem of the MILP. To do so, we propose a concrete twostep algorithm, and demonstrate empirical gains when optimizing generalized Gomory mixedinteger inequalities over various classes of MILPs. (Joint work with Didier Chételat.)

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTLarge Neighborhood Search for ILPs with Relaxationbased and ContrastiveLearningbased Heuristics11th Floor Lecture Hall
 Virtual Speaker
 Bistra Dilkina, University of Southern California
 Session Chair
 Tobias Achterberg, Gurobi Optimization
Abstract
Large Neighborhood Search (LNS) is an effective heuristic algorithm for finding high quality solutions of combinatorial optimization problems, including for largescale Integer Linear Programs (ILPs). It starts with an initial solution to the problem and iteratively improves it by searching a large neighborhood around the current best solution. LNS relies on destroy heuristics to select neighborhoods to search in by unassigning a subset of the variables and then reoptimizing their assignment. We focus on designing effective and efficient heuristics in LNS for integer linear programs (ILP). Local Branching (LB) is an heuristic that selects the neighborhood that leads to the largest improvement over the current solution in each iteration of LNS (the optimal subset of variables to ‘destroy’ within the Hamming ball of the incumbent solutions). LB is often slow since it needs to solve an ILP of the same size as input. First we propose LBrelaxationbased heuristics that compute as effective neighborhoods as LB but run faster and achieve stateoftheart anytime performance on several ILP benchmarks. Next, we propose a novel MLbased LNS for ILPs, namely CL, that uses contrastive learning (CL) to learn to imitate the LB heuristic. We not only use the optimal subsets provided by LB as the expert demonstration, but also leverage intermediate solutions and perturbations to collect sets of positive and negative samples. We use graph attention networks and a richer set of features to further improve its performance. Empirically, CL outperforms stateoftheart ML and nonML approaches at different runtime cutoffs in terms of multiple metrics, including the primal gap, the primal integral, the best performing rate and the survival rate, and achieves good generalization performance.

12:30  2:30 pm EDTLunch/Free Time
Monday, May 1, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

9:00  9:45 am EDTA comparative study of reformulations for piecewiseconvex optimizationSeminar  11th Floor Lecture Hall
 Renan Spencer Trindade, École Polytechnique, France
Abstract
Our research focuses on mixed integer nonlinear programming problems (MINLP) in which all nonconvex functions are univariate and separable. We employ the Sequential Convex MINLP technique to solve this class of problems to obtain a global optimal solution. This method uses piecewise linear relaxation, where only the concave parts are replaced by linear functions. In contrast, the convex intervals are handled by generating cut planes using the perspective cuts. This work presents a comprehensive theoretical and computational analysis of the different possible reformulations to the original problem. We show and demonstrate that while they are equivalent in the case of purely linear problems, they are not equivalent when considering nonlinear convex intervals

9:45  10:30 am EDTMathematical optimization at the service of classification and regression treesSeminar  11th Floor Lecture Hall
 Cristina MoleroRío, École Polytechnique
Abstract
Contrary to classic classification and regression trees, built in a greedy heuristic manner, designing the tree model through an optimization problem allows us to easily include desirable properties in Machine Learning in addition to prediction accuracy. In this talk, we present a Continuous Optimization approach that is scalable with respect to the size of the training sample, and illustrate this flexibility to model several important issues in Explainable and Fair Machine Learning. These include sparsity, as a proxy for interpretability, by reducing the amount of information necessary to predict well; fairness, by aiming to avoid predictions that discriminate against sensitive features such as gender or race; the costsensitivity for groups of individuals in which prediction errors are more critical, such as patients of a disease, by ensuring an acceptable accuracy performance for them; local explainability, where the goal is to identify the predictor variables that have the largest impact on the individual predictions; as well as data complexity in the form of observations of functional nature. The performance of our approach is illustrated on real and synthetic data sets.

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, May 2, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

8:30  9:00 am EDTClosing BreakfastCoffee Break  11th Floor Collaborative Space

9:00  9:20 am EDTHow to best slice a polytope11th Floor Lecture Hall
 Chiara Meroni, ICERM

9:25  9:45 am EDTUnification and extension: Solving subclasses of linear programs11th Floor Lecture Hall
 Bento Natura, Georgia Tech

9:45  10:00 am EDTBreakCoffee Break

10:00  10:20 am EDTRandom Shadows of Fixed Polytopes11th Floor Lecture Hall
 Alex Black, UC Davis

10:25  10:45 am EDTWriting integer PSD matrices as rankone sums11th Floor Lecture Hall
 Shixuan Zhang, Brown University

10:45  11:00 am EDTBreakCoffee Break

11:00  11:20 am EDTInformation complexity, branchandcut and GNNs11th Floor Lecture Hall
 Amitabh Basu, Johns Hopkins University

11:25  11:45 am EDTOn principal partition sequences of submodular functions11th Floor Lecture Hall
 Karthekeyan Chandrasekaran, University of Illinois UrbanaChampaign

11:45 am  12:00 pm EDTBreakCoffee Break

12:00  12:45 pm EDTI was kicking myself when I saw what you did11th Floor Lecture Hall
 Jon Lee, University of Michigan
Abstract
I will talk about these four papers, all over 30 years old, which have a total of 18 googlescholar citations, most being self citations.
1) J.L. A spectral approach to polyhedral dimension. Mathematical Programming, Series A, 47(3):441459, 1990. 2) J.L. Canonical equation sets for classes of concordant polytopes. Discrete Applied Mathematics, 28(3):207221, 1990. 3) J.L. Characterizations of the dimension for classes of concordant polytopes. Mathematics of Operations Research, 15(1):139154, 1990. 4) J.L and Yew Sing Lee. A spectral method for concordant polyhedral faces. Linear Algebra and its Applications, 159:1141, 1991. 
1:00  2:00 pm EDTEnd of Semester Networking LunchWorking Lunch  11th Floor Collaborative Space

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, May 3, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, May 4, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
Friday, May 5, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space
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Publications
 MarieCharlotte Brandenburg, Jesús A. De Loera, Chiara Meroni, The Best Ways to Slice a Polytope, arXiv:2304.14239, 2023.