Integer Programming Models for Round Robin Tournaments

Round robin tournaments are omnipresent in sport competitions and beyond. We propose two new integer programming formulations for scheduling a round robin tournament, one of which we call the matching formulation. We analytically compare their linear relaxations with the linear relaxation of a well-known traditional formulation. We find that the matching formulation is stronger than … Read more

Continuity of the conic hull

In a real Hilbert space V, the conic hull of G is the set cone(G) consisting of all nonnegative linear combinations of elements of G. Many optimization problems are sensitive to the changes in cone(G) that result from changes in G itself. Motivated by one such problem, we derive necessary and sufficient conditions for the … Read more

The Largest Unsolved QAP Instance Tai256c Can Be Converted into A 256-dimensional Simple BQOP with A Single Cardinality Constraint

Tai256c is the largest unsolved quadratic assignment problem (QAP) instance in QAPLIB; a 1.48\% gap remains between the best known feasible objective value and lower bound of the unknown optimal value. This paper shows that the instance can be converted into a 256 dimensional binary quadratic optimization problem (BQOP) with a single cardinality constraint which … Read more

Improving reliability with optimal allocation of maintenance resources: an application to power distribution networks

Power distribution networks should strive for reliable delivery of energy. In this paper, we support this endeavor by addressing the Maintenance Resources Allocation Problem (MRAP). This problem consists of scheduling preventive maintenance plans on the equipment of distribution networks for a planning horizon, seeking the best trade-offs between system reliability and maintenance budgets. We propose … Read more

On the Exactness of Dantzig-Wolfe Relaxation for Rank Constrained Optimization Problems

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 m two-sided linear constraints. Replacing the domain set by its closed convex hull offers us a convex Dantzig-Wolfe Relaxation (DWR) of the RCOP. Our goal is to characterize … Read more

Finding Groups with Maximum Betweenness Centrality via Integer Programming with Random Path Sampling

One popular approach to access the importance/influence of a group of nodes in a network is based on the notion of centrality. For a given group, its group betweenness centrality is computed, first, by evaluating a ratio of shortest paths between each node pair in a network that are “covered” by at least one node … Read more

Simple Alternating Minimization Provably Solves Complete Dictionary Learning

This paper focuses on complete dictionary learning problem, where the goal is to reparametrize a set of given signals as linear combinations of atoms from a learned dictionary. There are two main challenges faced by theoretical and practical studies of dictionary learning: the lack of theoretical guarantees for practically-used heuristic algorithms, and their poor scalability … Read more

A Consensus-Based Alternating Direction Method for Mixed-Integer and PDE-Constrained Gas Transport Problems

We consider dynamic gas transport optimization problems, which lead to large-scale and nonconvex mixed-integer nonlinear optimization problems (MINLPs) on graphs. Usually, the resulting instances are too challenging to be solved by state-of-the-art MINLP solvers. In this paper, we use graph decompositions to obtain multiple optimization problems on smaller blocks, which can be solved in parallel … Read more

Decentralized Stochastic Bilevel Optimization with Improved Per-Iteration Complexity

Bilevel optimization recently has received tremendous attention due to its great success in solving important machine learning problems like meta learning, reinforcement learning, and hyperparameter optimization. Extending single-agent training on bilevel problems to the decentralized setting is a natural generalization, and there has been a flurry of work studying decentralized bilevel optimization algorithms. However, it … Read more

Optimal Extragradient-Based Stochastic Bilinearly-Coupled Saddle-Point Optimization

We consider the smooth convex-concave bilinearly-coupled saddle-point problem, $\min_{\mathbf{x}}\max_{\mathbf{y}}~F(\mathbf{x}) + H(\mathbf{x},\mathbf{y}) – G(\mathbf{y})$, where one has access to stochastic first-order oracles for $F$, $G$ as well as the bilinear coupling function $H$. Building upon standard stochastic extragradient analysis for variational inequalities, we present a stochastic \emph{accelerated gradient-extragradient (AG-EG)} descent-ascent algorithm that combines extragradient and Nesterov’s … Read more