A convex cone is homogeneous if its automorphism group acts transitively on the interior of the cone, i.e., for every pair of points in the interior of the cone, there exists a cone automorphism that maps one point to the other. Cones that are homogeneous and self-dual are called symmetric. The symmetric cones include the … Read more
We consider the proximal-gradient method for minimizing an objective function that is the sum of a smooth function and a non-smooth convex function. A feature that distinguishes our work from most in the literature is that we assume that the associated proximal operator does not admit a closed-form solution. To address this challenge, we study … Read more
Two-stage stochastic programs with binary recourse are challenging to solve and efficient solution methods for such problems have been limited. In this work, we generalize an existing binary decision diagram-based (BDD-based) approach of Lozano and Smith (Math. Program., 2018) to solve a special class of two-stage stochastic programs with binary recourse. In this setting, the … Read more
We study continuous, equality knapsack problems with uniform separable, non-convex objective functions that are continuous, strictly increasing, antisymmetric about a point, and have concave and convex regions. For example, this model captures a simple allocation problem with the goal of optimizing an expected value where the objective is a sum of cumulative distribution functions of … Read more
Handling symmetries in optimization problems is essential for devising efficient solution methods. In this article, we present a general framework that captures many of the already existing symmetry handling methods. While these methods are mostly discussed independently from each other, our framework allows to apply different methods simultaneously and thus outperforming their individual effect. Moreover, … Read more
During the last decades, the use of advanced optimization algorithms to generate sports timetables has caught the attention of both academics and practitioners. From a managerial standpoint, the competition’s structure and the design of the league’s schedule represent key strategic decisions with a direct impact in terms of revenue and other important indicators. Argentina’s National … Read more
We study mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We present MIP relaxation methods for non-convex continuous variable products. In Part I, we consider MIP relaxations based on separable reformulation. The main focus is the introduction of the enhanced separable MIP relaxation for non-convex quadratic products … Read more
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
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
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