Related papers: Consistency Cuts for Dantzig-Wolfe Reformulations
In [SIAM J. Optim., 2022], the authors introduced a new linear programming (LP) relaxation for K-means clustering. In this paper, we further investigate both theoretical and computational properties of this relaxation. As evident from our…
Two-stage stochastic mixed-integer linear programs with mixed-integer recourse arise in many practical applications but are computationally challenging due to their large size and the presence of integer decisions in both stages. The…
We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection,…
We clarify the existence of two different types of truncations of the field content in a theory, the consistency of each type being achieved by different means. A proof is given of the conditions to have a consistent truncation in the case…
Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer…
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A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
Many problems in robust control and motion planning can be reduced to either find a sound approximation of the solution space determined by a set of nonlinear inequalities, or to the ``guaranteed tuning problem'' as defined by Jaulin and…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
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Benders decomposition is widely used to solve large mixed-integer problems. This paper takes advantage of machine learning and proposes enhanced variants of Benders decomposition for solving two-stage stochastic security-constrained unit…
The snags in Nucci(1996)REDUCE algorithm are the intrinsic computational efforts and the ability to recognize the ignorable variable(s) during the reduction process of the algorithm. An inappropriate choice of the ignorable variable(s)may…
Several well known large scale linear programming decomposition methodologies exist. Benders Decomposition, which covers the case where some small subset of variables link the otherwise separable subproblems. Dantzig-Wolfe decomposition and…
We study a mixed integer linear program with m integer variables and k non-negative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Andersen, Louveaux, Weismantel and Wolsey [Inequalities…
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Chance-constrained programming is a widely used framework for decision-making under uncertainty, yet its mixed-integer reformulations involve nonconvex mixing sets with a knapsack constraint, leading to weak relaxations and computational…
Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced $k$-cut of the graph, are…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
We develop a high order cut finite element method for the Stokes problem based on general inf-sup stable finite element spaces. We focus in particular on composite meshes consisting of one mesh that overlaps another. The method is based on…
This paper is concerned with a class of stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. For this class of problems, we investigate the consistency of optimal values and solutions…