We propose two new classes of valid inequalities (VIs) for the binary knapsack polytope, based on non-minimal covers. We also show that these VIs can be obtained through neither sequential nor simultaneous lifting of well-known cover inequalities. We further provide conditions under which they are facet-defining. The usefulness of these VIs is demonstrated using computational … Read more
We consider the solution of nonconvex quadratic optimization problems using an outer approximation of the set-copositive cone that is iteratively strengthened with conic constraints and cutting planes. Our methodology utilizes an MILP-based oracle for a generalization of the copositive cone that considers additional linear equality constraints. In numerical testing we evaluate our algorithm on a … Read more
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is still significantly harder to solve than a similar-size Linear Program (LP). It is well-known that a semidefinite program can be written as an LP … Read more
Bilevel optimization has gained significant attention in recent years due to its broad applications in machine learning. This paper focuses on bilevel optimization in decentralized networks and proposes a novel single-loop algorithm for solving decentralized bilevel optimization with a strongly convex lower-level problem. Our approach is a fully single-loop method that approximates the hypergradient using … Read more
We consider linear relaxations for multilinear optimization problems. In a recent paper, Khajavirad proved that the extended flower relaxation is at least as strong as the relaxation of any recursive McCormick linearization (Operations Research Letters 51 (2023) 146-152). In this paper we extend the result to more general linearizations, and present a simpler proof. Moreover, … Read more
This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers, i.e., without any roundoff errors or numerical tolerances. By integrating the method of precision boosting inside an LP iterative refinement loop, the combined algorithm is able to leverage the strengths of both methods: … Read more
We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least squares regression problem. We show that this formulation recovers ridge regression exactly and establishes the missing link between robust optimization and the mean squared error … Read more
Symmetry handling inequalities (SHIs) are an appealing and popular tool for handling symmetries in integer programming. Despite their practical application, little is known about their interaction with optimization problems. This article focuses on Schreier-Sims (SST) cuts, a recently introduced family of SHIs, and investigate their impact on the computational and polyhedral complexity of optimization problems. … Read more
We present generalizations of Newton’s method that incorporate derivatives of an arbitrary order \(d\) but maintain a polynomial dependence on dimension in their cost per iteration. At each step, our \(d^{\text{th}}\)-order method uses semidefinite programming to construct and minimize a sum of squares-convex approximation to the \(d^{\text{th}}\)-order Taylor expansion of the function we wish to … Read more
LTL freight carriers operate consolidation networks that utilize cross-docking terminals to facilitate thetransfer of freight between trailers and enhance trailer utilization. This research addresses the problem ofdetermining an optimal schedule for unloading inbound trailers at specific unloading doors using teams ofdock workers. The optimization objective is chosen to ensure that outbound trailers are loaded with … Read more