Monday, January 30, 2023

• 8:30 - 9:30 am EST

  Check In

  11th Floor Collaborative Space

• 9:30 - 9:50 am EST

  Check In

  11th Floor Collaborative Space
• 9:50 - 10:00 am EST

  Welcome

  11th Floor Lecture Hall

  • Brendan Hassett, ICERM/Brown University
• 10:00 - 11:00 am EST

  Matching Theory and School Choice

  Seminar - 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.

  • Video
  • Slides
• 11:00 - 11:30 am EST

  Coffee Break

  11th Floor Collaborative Space
• 11:30 am - 12:30 pm EST

  Matching Theory and School Choice

  Seminar - 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.

  • Video
  • Slides
• 12:30 - 2:30 pm EST

  Lunch/Free Time
• 2:30 - 3:30 pm EST

  Binary polynomial optimization: theory, algorithms, and applications

  Seminar - 11th Floor Lecture Hall

  • Speaker
  • Aida Khajavirad, Lehigh University

  • Session Chair
  • Marcia Fampa, Federal University of Rio de Janeiro

  Abstract

  In this mini-course, 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 higher-order Markov random fields, and demonstrate how our theoretical findings enable us to obtain efficient algorithms with theoretical performance guarantees for these applications.

  • Video
• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space
• 4:00 - 5:00 pm EST

  Binary polynomial optimization: theory, algorithms, and applications

  Seminar - 11th Floor Lecture Hall

  • Speaker
  • Aida Khajavirad, Lehigh University

  • Session Chair
  • Marcia Fampa, Federal University of Rio de Janeiro

  Abstract

  In this mini-course, 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 higher-order Markov random fields, and demonstrate how our theoretical findings enable us to obtain efficient algorithms with theoretical performance guarantees for these applications.

  • Video
• 5:00 - 6:30 pm EST

  Reception

  11th Floor Collaborative Space

Tuesday, January 31, 2023

• 9:00 - 10:00 am EST

  Approximation Algorithms for Network Design Problems

  Seminar - 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 2-approximation 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 better-than-2 approximation algorithm for Weighted Connectivity Augmentation.

  • Video
• 10:00 - 10:30 am EST

  Coffee Break

  11th Floor Collaborative Space
• 10:30 - 11:30 am EST

  Approximation Algorithms for Network Design Problems

  Seminar - 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 2-approximation 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 better-than-2 approximation algorithm for Weighted Connectivity Augmentation.

  • Video
• 11:45 am - 1:00 pm EST

  Problem Session

  11th Floor Lecture Hall
• 1:00 - 3:00 pm EST

  Lunch/Free Time
• 3:00 - 5:00 pm EST

  Poster Session / Coffee Break

  Poster Session - 11th Floor Collaborative Space

  • Slides

Wednesday, February 1, 2023

• 9:00 - 10:00 am EST

  Polynomial optimization on finite sets

  Seminar - 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 n-variables. 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 self-contained introduction to this vibrant and exciting research area.

  • Video Available Soon
  • Slides
  • Problem Sheet
• 10:00 - 10:30 am EST

  Coffee Break

  11th Floor Collaborative Space
• 10:30 - 11:30 am EST

  Polynomial optimization on finite sets

  Seminar - 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 n-variables. 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 self-contained introduction to this vibrant and exciting research area.

  • Live Stream
  • Slides
• 11:40 - 11:45 am EST

  Group Photo

  11th Floor Lecture Hall
• 11:45 am - 2:00 pm EST

  Lunch/Free Time
• 2:00 - 3:00 pm EST

  Matching Theory and School Choice

  Seminar - 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.

  • Live Stream
  • Slides
• 3:00 - 3:30 pm EST

  Coffee Break

  11th Floor Collaborative Space
• 3:30 - 4:30 pm EST

  Matching Theory and School Choice

  Seminar - 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.

  • Live Stream
  • Slides

Thursday, February 2, 2023

• 9:00 - 10:00 am EST

  Approximation Algorithms for Network Design Problems

  Seminar - 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 2-approximation 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 better-than-2 approximation algorithm for Weighted Connectivity Augmentation.
• 10:00 - 10:30 am EST

  Coffee Break

  11th Floor Collaborative Space
• 10:30 - 11:30 am EST

  Approximation Algorithms for Network Design Problems

  Seminar - 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 2-approximation 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 better-than-2 approximation algorithm for Weighted Connectivity Augmentation.
• 11:30 am - 1:30 pm EST

  Lunch/Free Time
• 1:30 - 2:30 pm EST

  Binary polynomial optimization: theory, algorithms, and applications

  Seminar - 11th Floor Lecture Hall

  • Speaker
  • Aida Khajavirad, Lehigh University

  • Session Chair
  • Marcia Fampa, Federal University of Rio de Janeiro

  Abstract

  In this mini-course, 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 higher-order 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 EST

  Coffee Break

  11th Floor Collaborative Space
• 3:30 - 4:30 pm EST

  Binary polynomial optimization: theory, algorithms, and applications

  Seminar - 11th Floor Lecture Hall

  • Speaker
  • Aida Khajavirad, Lehigh University

  • Session Chair
  • Marcia Fampa, Federal University of Rio de Janeiro

  Abstract

  In this mini-course, 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 higher-order 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 EST

  Polynomial optimization on finite sets

  Seminar - 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 n-variables. 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 self-contained introduction to this vibrant and exciting research area.
• 11:00 - 11:30 am EST

  Coffee Break

  11th Floor Collaborative Space
• 11:30 am - 12:30 pm EST

  Polynomial optimization on finite sets

  Seminar - 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 n-variables. 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 self-contained introduction to this vibrant and exciting research area.
• 12:30 - 2:30 pm EST

  Lunch/Free Time
• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Monday, February 6, 2023

• 9:30 - 10:00 am EST

  ICERM Director and Organizer Welcome

  Welcome - 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, Otto-von-Guericke Universität Magdeburg
  • Jon Lee, University of Michigan
• 3:30 - 4:30 pm EST

  Informal Tea

  Coffee Break - 11th Floor Collaborative Space

Tuesday, February 7, 2023

• 9:30 - 10:30 am EST

  Director/Organizer Meeting

  Meeting - 11th Floor Conference Room
• 12:00 - 1:00 pm EST

  Postdoc/Graduate Student Meeting with ICERM Director

  Meeting - 11th Floor Lecture Hall
• 2:30 - 3:30 pm EST

  Meet to organize the mother of all seminar(s)

  Meeting - 11th Floor Lecture Hall
• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Wednesday, February 8, 2023

• 10:00 am - 12:00 pm EST

  Postdoc/ Grad Introductions

  11th Floor Lecture Hall
• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Thursday, February 9, 2023

• 10:00 am - 12:00 pm EST

  Postdoc/ Grad Introductions

  11th Floor Lecture Hall
• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Friday, February 10, 2023

• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Monday, February 13, 2023

• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Tuesday, February 14, 2023

• 9:00 - 10:00 am EST

  Professional Development: Ethics I

  Professional Development - 11th Floor Lecture Hall
• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Wednesday, February 15, 2023

• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Thursday, February 16, 2023

• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Friday, February 17, 2023

• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Tuesday, February 21, 2023

• 9:00 - 10:00 am EST

  Professional Development: Ethics II

  Professional Development - 11th Floor Lecture Hall
• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Wednesday, February 22, 2023

• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Thursday, February 23, 2023

• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Friday, February 24, 2023

• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Monday, February 27, 2023

• 8:50 - 9:00 am EST

  Welcome

  11th Floor Lecture Hall

  • Brendan Hassett, ICERM/Brown University
• 9:00 - 9:45 am EST

  On Constrained Mixed-Integer DR-Submodular Minimization

  11th 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 non-convex and non-concave. We study the problem of minimizing any DR-submodular 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 DR-submodular 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 polynomial-time exact separation algorithm for our proposed valid inequalities, with which we first establish the polynomial-time solvability of this class of mixed-integer nonlinear optimization problems. This is joint work with Kim Yu.
• 10:00 - 10:30 am EST

  Coffee Break

  11th Floor Collaborative Space
• 10:30 - 11:15 am EST

  Semidefinite Optimization with Eigenvector Branching

  11th 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 X-xx' is positive semidefinite to obtain a convex relaxation of the condition X=xx', where x is an n-vector. We consider a new hyperplane branching method for SDP based on using an eigenvector of X-xx'. 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 two-trust-region subproblem.
• 11:30 am - 12:15 pm EST

  A Breakpoints Based Method for the Maximum Diversity and Dispersion Problems

  11th 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 greedy-like 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 non-perturbed 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 Gurobi--an 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 EST

  Lunch/Free Time
• 2:30 - 3:15 pm EST

  Approximating integer programs with monomial orders

  11th 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 outer-approximations 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 inner-approximations 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 EST

  Coffee Break

  11th Floor Collaborative Space
• 4:00 - 4:45 pm EST

  Solving ACOPF problems

  11th 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 on-going GO competition for solving modern, large-scale versions of ACOPF which include scenario constraints and integer variables. Second, we will outline challenges to state-of-the-art MINLP solvers based on spatial branch-and-bound that arise in ACOPF instances. Finally we will discuss some fundamental issues related to numerical precision.
• 5:00 - 6:30 pm EST

  Reception

  11th Floor Collaborative Space

Tuesday, February 28, 2023

• 9:00 - 9:45 am EST

  Maximal quadratic free sets: basic constructions and steps towards a full characterization

  11th 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 S-free sets, and inclusion-wise maximal S-free sets yield the strongest intersection cuts. When S is a lattice, maximal S-free sets are well-studied 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 quadratic-free sets. Additionally, we explore how to generalize the basic procedure to construct a plethora of new maximal quadratic-free sets for homogeneous quadratics. Joint work with Joseph Paat and Felipe Serrano.
• 10:00 - 10:30 am EST

  Coffee Break

  11th Floor Collaborative Space
• 10:30 - 11:15 am EST

  From micro to macro structure: a journey in company of the Unit Commitment problem

  11th 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 full-problem size with the definition of strong but large formulations (and the nontrivial trade-offs they entail), and finally skyrocketing to large- and huge-scale problems (stochastic UC, stochastic reservoirs optimization, long-term energy system design) where UC (and its sub-structures) 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 Star-Shaped MINLPs, but it will also try to give a broad-brush of the larger picture, with some time devoted to discussing the nontrivial implications of actually implementing solution methods for huge-scale 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 EST

  TBA

  11th Floor Lecture Hall

  • Speaker
  • Ricardo Fukasawa, University of Waterloo

  • Session Chair
  • Daniel Bienstock, Columbia University
• 12:30 - 2:30 pm EST

  Lunch/Free Time
• 2:30 - 3:15 pm EST

  Network Design Queueing MINLP: Models, Reformulations, and Algorithms

  11th Floor Lecture Hall

  • Speaker
  • Miguel Lejeune, George Washington University

  • Session Chair
  • Merve Bodur, University of Toronto

  Abstract

  We present several queueing-based 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 warm-start component, new optimality-based 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 drone-based delivery of automated external defibrillators to out-of-hospital cardiac arrests (OHCA) and naloxone to opioid overdoses. The computational experiments are based on real-life 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 EST

  Coffee Break

  11th Floor Collaborative Space
• 4:00 - 4:45 pm EST

  TBA

  11th 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 EST

  Minimizing quadratics over integers

  11th Floor Lecture Hall

  • Speaker
  • Alberto Del Pia, University of Wisconsin-Madison

  • 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 EST

  Coffee Break

  11th Floor Collaborative Space
• 10:30 - 11:15 am EST

  Optimizing for Equity in Urban Planning

  11th 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 Kolm-Pollak 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 Kolm-Pollak EDE is designed to penalize for inequity. In this talk, we explore the problem of finding an optimal distribution from various alternatives using the Kolm-Pollak EDE to quantify optimal. Unfortunately, optimizing over the Kolm-Pollak 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 Kolm-Pollak 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 EST

  Explicit convex hull description of bivariate quadratic sets with indicator variables

  11th 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 branch-and-cut based solvers to enhance the quality of existing relaxations.
• 12:15 - 12:20 pm EST

  Group Photo - i=Immediately following talk

  Group Photo - 11th Floor Lecture Hall
• 12:30 - 2:30 pm EST

  Lunch/Free Time
• 2:30 - 3:30 pm EST

  Poster Session

  11th Floor Collaborative Space
• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space
• 4:00 - 4:45 pm EST

  Matrix Completion over GF(2) with Applications to Index Coding

  11th Floor Lecture Hall

  • Speaker
  • Jeff Linderoth, University of Wisconsin-Madison

  • Session Chair
  • Kurt Anstreicher, University of Iowa

  Abstract

  We discuss integer-programming-based approaches to doing low-rank 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 integer-valued 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 EST

  Dantzig-Wolfe Bound by Cutting Planes

  11th Floor Lecture Hall

  • Speaker
  • Oktay Gunluk, Cornell University

  • Session Chair
  • Yuan Zhou, University of Kentucky

  Abstract

  Dantzig-Wolfe (DW) decomposition is a well-known technique in mixed-integer 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 branch-and-cut 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 EST

  Coffee Break

  11th Floor Collaborative Space
• 10:30 - 11:15 am EST

  Number of inequalities in integer-programming descriptions of a set

  11th 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 EST

  Reciprocity between tree ensemble optimization and multilinear optimization

  11th 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 multi-commodity transportation problems with costs modeled using tree ensembles shows the practical advantage of our formulation relative to existing formulations of tree ensembles and other piecewise-linear modeling techniques. We then consider piecewise polyhedral relaxation of multilinear optimization problems. We provide the first ideal formulation over non-regular 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 EST

  Lunch/Free Time
• 2:30 - 3:15 pm EST

  Integer Semidefinite Programming - a New Perspective

  11th Floor Lecture Hall

  • Speaker
  • Renata Sotirov, Tilburg University

  • Session Chair
  • Fatma Kılınç-Karzan, 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\'atal-Gomory (CG) cutting-plane procedure to ISDPs. We also show how to exploit CG cuts in a branch-and-cut framework for ISDPs. Finally, we demonstrate the practical strength of the CG cuts in our branch-and-cut algorithm. Our results provide a new perspective on ISDPs.
• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space
• 4:00 - 4:45 pm EST

  TBA

  11th Floor Lecture Hall

  • Speaker
  • Alper Atamturk, University of California - Berkeley

  • Session Chair
  • Fatma Kılınç-Karzan, Carnegie Mellon University

Friday, March 3, 2023

• 9:00 - 9:45 am EST

  Markov Chain-based Policies for Multi-stage Stochastic Integer Linear Programming

  11th 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 multi-stage stochastic programs with mixed-integer 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 branch-and-cut 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 two-stage linear decision rule (2SLDR) approximations and propose MC-based variants to obtain high-quality 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 EST

  Coffee Break

  11th Floor Collaborative Space
• 10:30 - 11:15 am EST

  On practical first order methods for LP

  11th 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 order-methods, 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 EST

  Lunch/Free Time
• 1:30 - 2:15 pm EST

  Ideal polyhedral relaxations of non-polyhedral sets

  11th Floor Lecture Hall

  • Speaker
  • Andres Gomez, University of Southern California

  • Session Chair
  • Marcia Fampa, Federal University of Rio de Janeiro

  Abstract

  Algorithms for mixed-integer 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 mixed-integer linear optimization problems, it is well-known 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, mixed-integer linear optimization problems deemed to be intractable 30 years old can be solved to optimality in seconds or minutes nowadays. Modern statistical and decision-making problems call for mixed-integer nonlinear optimization (MINLO) formulations, which inherently lead to non-polyhedral relaxations. There has been a substantial progress in extending and adapting techniques for both the mixed-integer 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 non-convexities associated with discrete variables. Thus, by exploiting this substructure, convexification theory and methods based on polyhedral theory can naturally be used study non-polyhedral sets. We also provide insights into how to design algorithms that tackle the ensuing relaxations.
• 2:30 - 3:15 pm EST

  On Dantzig-Wolfe Relaxation of Rank Constrained Optimization: Exactness, Rank Bounds, and Algorithms

  11th 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 two-sided linear matrix inequalities. The generic RCOP framework exists in many nonconvex optimization and machine learning problems. Although RCOP is, in general, NP-hard, recent studies reveal that its Dantzig-Wolfe 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 first-known 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 EST

  Coffee Break

  11th Floor Collaborative Space

Monday, March 6, 2023

• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Tuesday, March 7, 2023

• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Wednesday, March 8, 2023

• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Thursday, March 9, 2023

• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Friday, March 10, 2023

• 3:30 - 4:00 pm EST

  Coffee Break

  11th Floor Collaborative Space

Monday, March 13, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Tuesday, March 14, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Wednesday, March 15, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Thursday, March 16, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Friday, March 17, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Monday, March 20, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Tuesday, March 21, 2023

• 9:00 - 10:00 am EDT

  Professional Development: Hiring Process

  Professional Development - 11th Floor Lecture Hall
• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Wednesday, March 22, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Thursday, March 23, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Friday, March 24, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Monday, April 3, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Tuesday, April 4, 2023

• 9:00 - 10:00 am EDT

  Professional Development: Papers and Journals

  Professional Development - 11th Floor Lecture Hall
• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Wednesday, April 5, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Thursday, April 6, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Friday, April 7, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Monday, April 10, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Tuesday, April 11, 2023

• 9:00 - 10:00 am EDT

  Professional Development: Job Applications

  Professional Development - 11th Floor Lecture Hall
• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Wednesday, April 12, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Thursday, April 13, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Friday, April 14, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Monday, April 17, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Tuesday, April 18, 2023

• 9:00 - 10:00 am EDT

  Professional Development: Grant Proposals

  Professional Development - 11th Floor Lecture Hall
• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Wednesday, April 19, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Thursday, April 20, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Friday, April 21, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Monday, May 1, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Tuesday, May 2, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Wednesday, May 3, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Thursday, May 4, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space

Friday, May 5, 2023

• 3:30 - 4:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space