Related papers: Relaxation strength for multilinear optimization: …
We consider a smooth pessimistic bilevel optimization problem, where the lower-level problem is convex and satisfies the Slater constraint qualification. These assumptions ensure that the Karush-Kuhn-Tucker (KKT) reformulation of our…
This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing…
Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However,…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
Disjunctive cutting planes can tighten a relaxation of a mixed-integer linear program. Traditionally, such cuts are obtained by solving a higher-dimensional linear program, whose additional variables cause the procedure to be…
In this work, we propose three Braess-Sarazin-type multigrid relaxation schemes for solving linear elasticity problems, where the marker and cell scheme, a finite difference method, is used for the discretization. The three relaxation…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
We give a combinatorial extension of the classical inequalities of Maclaurin about symmetric functions of several variables. We discuss two problems - one analytical and another combinatorial - and show that they are in some sense…
We begin with an improvement to an extension result for subharmonic functions of Blanchet et al. With the aid of this improvement we then give extension results for subharmonic functions, for separately subharmonic functions, for harmonic…
Many ranking and agent trace datasets are recorded as linear orders even though their latent structure is only partially ordered. This is especially common in agent and workflow traces, where observed order may reflect arbitrary…
In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…
Stability analysis of Wilkinson's iterative refinement with a relaxation IR(omega) for solving linear systems is given. It extends existing results for omega=1, i.e., for Wilkinson's iterative refinement. We assume that all computations are…
Relaxation theorems which apply to one, two and three-dimensional nonlinear elasticity are proved. We take into account the fact an infinite amount of energy is required to compress a finite line, surface or volume into zero line, surface…
We study semidefinite programming (SDP) relaxations for the NP-hard problem of globally optimizing a quadratic function over the Stiefel manifold. We introduce a strengthened relaxation based on two recent ideas in the literature: (i) a…
We prove that we can always construct strongly minimal linearizations of an arbitrary rational matrix from its Laurent expansion around the point at infinity, which happens to be the case for polynomial matrices expressed in the monomial…
We consider linear programs involving uncertain parameters and propose a new tractable robust counterpart which contains and generalizes several other models including the existing Affinely Adjustable Robust Counterpart and the Fully…
Optimal power flow (OPF) is a key problem in power system operations. OPF problems that use the nonlinear AC power flow equations to accurately model the network physics have inherent challenges associated with non-convexity. To address…
The demand for classical-quantum hybrid algorithms to solve large-scale combinatorial optimization problems using quantum annealing (QA) has increased. One approach involves obtaining an approximate solution using classical algorithms and…
In this paper, we study the convex quadratic optimization problem with indicator variables. For the bivariate case, we describe the convex hull of the epigraph in the original space of variables, and also give a conic quadratic extended…