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Bibliographic Details
Main Authors: Locatelli, Marco, Piccialli, Veronica, Sudoso, Antonio M.
Format: Preprint
Published: 2022
Subjects:
Online Access:https://arxiv.org/abs/2211.08911
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author Locatelli, Marco
Piccialli, Veronica
Sudoso, Antonio M.
author_facet Locatelli, Marco
Piccialli, Veronica
Sudoso, Antonio M.
contents In this paper, we propose a branch-and-bound algorithm for solving nonconvex quadratic programming problems with box constraints (BoxQP). Our approach combines existing tools, such as semidefinite programming (SDP) bounds strengthened through valid inequalities, with a new class of optimality-based linear cuts which leads to variable fixing. The most important effect of fixing the value of some variables is the size reduction along the branch-and-bound tree, allowing to compute bounds by solving SDPs of smaller dimension. Extensive computational experiments over large dimensional (up to $n=200$) test instances show that our method is the state-of-the-art solver on large-scale BoxQPs. Furthermore, we test the proposed approach on the class of binary QP problems, where it exhibits competitive performance with state-of-the-art solvers.
format Preprint
id arxiv_https___arxiv_org_abs_2211_08911
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Fix and Bound: An efficient approach for solving large-scale quadratic programming problems with box constraints
Locatelli, Marco
Piccialli, Veronica
Sudoso, Antonio M.
Optimization and Control
In this paper, we propose a branch-and-bound algorithm for solving nonconvex quadratic programming problems with box constraints (BoxQP). Our approach combines existing tools, such as semidefinite programming (SDP) bounds strengthened through valid inequalities, with a new class of optimality-based linear cuts which leads to variable fixing. The most important effect of fixing the value of some variables is the size reduction along the branch-and-bound tree, allowing to compute bounds by solving SDPs of smaller dimension. Extensive computational experiments over large dimensional (up to $n=200$) test instances show that our method is the state-of-the-art solver on large-scale BoxQPs. Furthermore, we test the proposed approach on the class of binary QP problems, where it exhibits competitive performance with state-of-the-art solvers.
title Fix and Bound: An efficient approach for solving large-scale quadratic programming problems with box constraints
topic Optimization and Control
url https://arxiv.org/abs/2211.08911