A branch-and-cut algorithm using polar cuts for solving nonconvex quadratic programming problems

In this paper, we propose a branch-and-cut algorithm for solving a nonconvex quadratically constrained quadratic programming (QCQP) problem with a nonempty bounded feasible domain. The problem is first transformed into a linear conic programming problem, and then approximated by semidefinite program...

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Bibliographic Details
Published in:Optimization Vol. 67; no. 2; pp. 359 - 375
Main Authors: Deng, Zhibin, Fang, Shu-Cherng, Lu, Cheng, Guo, Xiaoling
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 01.02.2018
Taylor & Francis LLC
Subjects:
Algorithms
Branch & bound algorithms
Branch-and-cut algorithm
Feasibility
Lower bounds
nonconvex quadratically constrained quadratic programming
Optimization
polar cut
Quadratic programming
Semidefinite programming
semidefinite relaxation
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:In this paper, we propose a branch-and-cut algorithm for solving a nonconvex quadratically constrained quadratic programming (QCQP) problem with a nonempty bounded feasible domain. The problem is first transformed into a linear conic programming problem, and then approximated by semidefinite programming problems over different intervals. In order to improve the lower bounds, polar cuts, generated from corresponding cut-generation problems, are embedded in a branch-and-cut algorithm to yield a globally - -optimal solution (with respect to feasibility and optimality, respectively) in a finite number of iterations. To enhance the computational speed, an adaptive branch-and-cut rule is adopted. Numerical experiments indicate that the number of explored nodes required for solving QCQP problems can be significantly reduced by employing the proposed polar cuts.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2017.1391253