Article

Journal of Global Optimization

, Volume 13, Issue 2, pp 151-170

First online:

A Polyhedral Approach for Nonconvex Quadratic Programming Problems with Box Constraints

  • Yasutoshi YajimaAffiliated withDepartment of Industrial Engineering and Management, Tokyo Institute of Technology
  • , Tetsuya FujieAffiliated withDepartment of Mathematical and Computing Sciences, Tokyo Institute of Technology

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Abstract

We apply a linearization technique for nonconvex quadratic problems with box constraints. We show that cutting plane algorithms can be designed to solve the equivalent problems which minimize a linear function over a convex region. We propose several classes of valid inequalities of the convex region which are closely related to the Boolean quadric polytope. We also describe heuristic procedures for generating cutting planes. Results of preliminary computational experiments show that our inequalities generate a polytope which is a fairly tight approximation of the convex region.

Cutting plane method Linearization technique Nonconvex quadratic programs Valid inequalities