Solving the canonical dual of box-and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm

  • Authors:

  • DavidYang Gao;LayneT. Watson;DavidR. Easterling;WilliamI. Thacker;StephenC. Billups

  • Affiliations:

  • Graduate School of Information Technology and Mathematical Science, University of Ballarat, PO Box 663, Ballarat, Victoria, 3353, Australia;Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA;Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA;Department of Computer Science, Winthrop University, Rock Hill, SC, 29733, USA;Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, CO, 80217-3364, USA

  • Venue:
  • Optimization Methods & Software
  • Year:
  • 2013

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Abstract

This paper presents a massively parallel global deterministic direct search method VTDIRECT for solving nonconvex quadratic minimization problems with either box or±1 integer constraints. Using the canonical dual transformation, these well-known NP-hard problems can be reformulated as perfect dual stationary problems with zero duality gap. Under certain conditions, these dual problems are equivalent to smooth concave maximization over a convex feasible space. Based on a perturbation method proposed by Gao, the integer programming problem is shown to be equivalent to a continuous unconstrained Lipschitzian global optimization problem. The parallel algorithm VTDIRECT is then applied to solve these dual problems to obtain global minimizers. Parallel performance results for several nonconvex quadratic integer programming problems are reported.