Relaxing the optimality conditions of box QP

Authors:
Samuel Burer;Jieqiu Chen
Affiliations:
Department of Management Sciences, University of Iowa, Iowa City, USA 52242-1994;Department of Management Sciences, University of Iowa, Iowa City, USA 52242-1994
Venue:
Computational Optimization and Applications
Year:
2011

Citing 4
Cited 0

A polyhedral study of nonconvex quadratic programs with box constraints

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A branch-and-cut algorithm for nonconvex quadratic programs with box constraints

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Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming

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Globally solving box-constrained nonconvex quadratic programs with semidefinite-based finite branch-and-bound

Computational Optimization and Applications

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Abstract

We present semidefinite relaxations of nonconvex, box-constrained quadratic programming, which incorporate the first- and second-order necessary optimality conditions, and establish theoretical relationships between the new relaxations and a basic semidefinite relaxation due to Shor. We compare these relaxations in the context of branch-and-bound to determine a global optimal solution, where it is shown empirically that the new relaxations are significantly stronger than Shor's. An effective branching strategy is also developed.