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

Tobias Achterberg
Gorubi OptimizationApr 2428, 2023

Hessa AlThani
University of MichiganJan 29Mar 18, 2023

Rachael Alfant
Rice UniversityApr 2428, 2023

Félix Almendra Hernández
UC DavisJan 30Feb 3, 2023

Miguel Anjos
University of EdinburghFeb 18May 6, 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

Ishan Bansal
Cornell UniversityJan 30Feb 3, 2023

Amitabh Basu
Johns Hopkins UniversityMar 26May 6, 2023

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

Hande Benson
Drexel UniversityFeb 27Mar 3, 2023

Dimitris Bertsimas
MITJan 30May 5, 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

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

Teressa Chambers
Brown UniversityJan 30Feb 3, 2023

Karthekeyan Chandrasekaran
University of Illinois UrbanaChampaignFeb 6May 6, 2023

Effrosyni Chasioti
Kent State UniversityJan 30May 6, 2023

Lin Chen
Texas Tech UniversityFeb 27Mar 3, 2023

Zhongzhu Chen
University of MichiganJan 30Mar 18, 2023

Gerard Cornuejols
Carnegie Mellon UniversityMar 19Apr 7, 2023

Francisco Criado Gallart
CUNEF UniversidadJan 30May 5, 2023

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

Daniel Dadush
Centrum Wiskunde & InformaticaMar 26Apr 28, 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; Jan 30May 6, 2023

Daniel de Roux
Carnegie Mellon UniversityFeb 26Mar 5, 2023

Alberto Del Pia
University of WisconsinMadisonFeb 26Mar 4, 2023

Santanu Dey
Georgia Institute of Technology.Mar 19May 5, 2023

Antoine Deza
McMaster UniversityMar 26Apr 22, 2023

Bistra Dilkina
University of Southern CaliforniaApr 2329, 2023

Alina Ene
Boston UniversityMar 2731, 2023

Daniel Espinoza
University of ChileFeb 26Mar 4, 2023

Yuri Faenza
Columbia UniversityJan 29Feb 2, 2023; Feb 68, 2023; Feb 1617, 2023; Feb 2324, 2023; Feb 27Mar 3, 2023; Mar 910, 2023; Mar 1219, 2023; Mar 2324, 2023; Mar 3031, 2023; Apr 67, 2023; Apr 1314, 2023; Apr 2021, 2023; Apr 2728, 2023; May 45, 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; Feb 27Mar 3, 2023

Antonio Frangioni
Università di PisaFeb 27Mar 3, 2023

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

Rohan Ghuge
University of MichiganJan 30Apr 3, 2023

Ambros Gleixner
Zuse Institute BerlinApr 2329, 2023

Michel Goemans
Massachusetts Institute of TechnologyJan 30May 5, 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

Anupam Gupta
Carnegie Mellon UniversityMar 2731, 2023

Swati Gupta
Georgia TechMar 26Apr 1, 2023; Apr 2428, 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

Ilyia 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

Klaus Jansen
Kiel UniversityFeb 26Apr 3, 2023

Sean Kafer
University of WaterlooJan 29May 7, 2023

Volker Kaibel
OttovonGuericke Universität MagdeburgApr 2029, 2023

Lennart Kauther
RWTH Aachen UniversityJan 29Feb 4, 2023

Aida Khajavirad
Lehigh UniversityJan 30Feb 3, 2023

Sammy Khalife
Johns Hopkins UniversityJan 30May 5, 2023

Fatma KılınçKarzan
Carnegie Mellon UniversityJan 30May 5, 2023; Feb 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

Kirill Kukharenko
Otto von Guericke University MagdeburgMar 2731, 2023

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

Anatoliy Kuznetsov
Georgia Institute of TechnologyFeb 27Mar 3, 2023

Jon Lee
University of MichiganJan 29May 6, 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

Feng Liu
Stevens Institute of TechnologyFeb 27Mar 2, 2023

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

Andrea Lodi
Cornell TechApr 330, 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

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

David Morton
Northwestern UniversityFeb 27Mar 2, 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

Ojas Parekh
Sandia National LaboratoriesApr 2329, 2023

Ethan Partida
BrownJan 30Feb 3, 2023

Britta Peis
RWTH Aachen UniversityMar 19Apr 3, 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

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 TechnologyApr 2329, 2023

Laura Sanità
Bocconi University of MilanJan 29Feb 4, 2023

Lisa Sauermann
MITMar 2731, 2023

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

Mohit Singh
Georgia TechMar 26Apr 8, 2023

Martin Skutella
TU BerlinMar 2631, 2023

Renata Sotirov
Tilburg UniversityFeb 26Mar 4, 2023

Emily Speakman
University of Colorado  DenverFeb 26Mar 4, 2023

Ola Svensson
EPFLMar 26Apr 1, 2023

Mohit Tawarmalani
Purdue UniversityFeb 27Mar 3, 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

Fei Wang
University of WaterlooJan 31Mar 1, 2023

Chengyang Wang
UC DavisJan 29Feb 4, 2023; Feb 26Mar 4, 2023; Mar 6May 5, 2023

Jie Wang
Georgia Institute of TechnologyFeb 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

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
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 Photo11th 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 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.
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 am  12:00 pm ESTPostdoc/ Grad Introductions11th 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 am  12:00 pm ESTPostdoc/ Grad Introductions11th 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

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

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

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

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

3:30  4:00 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
 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 ESTTBA11th Floor Lecture Hall
 Speaker
 Ricardo Fukasawa, University of Waterloo
 Session Chair
 Daniel Bienstock, Columbia University

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 ESTTBA11th Floor Lecture Hall
 Virtual Speaker
 Matthias Köppe, UC Davis
 Session Chair
 Merve Bodur, University of Toronto
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.

12:15  12:20 pm ESTGroup Photo  i=Immediately following talkGroup Photo  11th Floor Lecture Hall

12:30  2:30 pm ESTLunch/Free Time

2:30  3:30 pm ESTPoster Session11th Floor Collaborative Space

3:30  4:00 pm ESTCoffee Break11th 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 ESTReciprocity between tree ensemble optimization and multilinear optimization11th Floor Lecture Hall
 Speaker
 Mohit Tawarmalani, Purdue University
 Session Chair
 Yuan Zhou, University of Kentucky
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.

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 ESTTBA11th Floor Lecture Hall
 Speaker
 Alper Atamturk, University of California  Berkeley
 Session Chair
 Fatma KılınçKarzan, Carnegie Mellon University
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, University of Chile
 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

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

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

3:30  4:00 pm EDTCoffee Break11th 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

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

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 EDTCoffee Break11th Floor Collaborative Space
Thursday, March 23, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

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, 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

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

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

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

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

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, May 1, 2023
Discrete Optimization: Mathematics, Algorithms, and Computation

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

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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 Already in the US?

F1 and J1 not sponsored by ICERM: obtain a letter approving reimbursement from the International Office of your home institution PRIOR to travel.
H1B holders do not need letter of approval.
All other visas: alert ICERM staff immediately about your situation.
ICERM does not reimburse visa fees. This chart is to inform visitors whether the visa they enter the US on allows them to receive reimbursement for the items outlined in their invitation letter.
Financial Support
This section is for general purposes only and does not indicate that all attendees receive funding. Please refer to your personalized invitation to review your offer.
 ORCID iD
 As this program is funded by the National Science Foundation (NSF), ICERM is required to collect your ORCID iD if you are receiving funding to attend this program. Be sure to add your ORCID iD to your Cube profile as soon as possible to avoid delaying your reimbursement.
 Acceptable Costs

 1 roundtrip between your home institute and ICERM
 Flights on U.S. or E.U. airlines – economy class to either Providence airport (PVD) or Boston airport (BOS)
 Ground Transportation to and from airports and ICERM.
 Unacceptable Costs

 Flights on nonU.S. or nonE.U. airlines
 Flights on U.K. airlines
 Seats in economy plus, business class, or first class
 Change ticket fees of any kind
 Multiuse bus passes
 Meals or incidentals
 Advance Approval Required

 Personal car travel to ICERM from outside New England
 Multipledestination plane ticket; does not include layovers to reach ICERM
 Arriving or departing from ICERM more than a day before or day after the program
 Multiple trips to ICERM
 Rental car to/from ICERM
 Flights on a Swiss, Japanese, or Australian airlines
 Arriving or departing from airport other than PVD/BOS or home institution's local airport
 2 oneway plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
 Travel Maximum Contributions

 New England: $250
 Other contiguous US: $750
 Asia & Oceania: $2,000
 All other locations: $1,500
 Note these rates were updated in Spring 2022 and superseded any prior invitation rates. Any invitations without travel support will still not receive travel support.
 Reimbursement Requests

Request Reimbursement with Cube
Refer to the back of your ID badge for more information. Checklists are available at the front desk and in the Reimbursement section of Cube.
 Reimbursement Tips

 Scanned original receipts are required for all expenses
 Airfare receipt must show full itinerary and payment
 ICERM does not offer per diem or meal reimbursement
 Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via pdf of Google Maps result
 Keep all documentation until you receive your reimbursement!
 Reimbursement Timing

6  8 weeks after all documentation is sent to ICERM. All reimbursement requests are reviewed by numerous central offices at Brown who may request additional documentation.
 Reimbursement Deadline

Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. Submissions after thirty days will incur applicable taxes. No submissions are accepted more than six months after the program end.