A Polyhedral Approach for Nonconvex Quadratic Programming Problemswith Box Constraints

Authors:
Yasutoshi Yajima;Tetsuya Fujie
Affiliations:
Department of Industrial Engineering and Management, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152-8552, Japan (e-mail: Email: yasutosi@me.titech.ac.jp);Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152-8552, Japan
Venue:
Journal of Global Optimization
Year:
1998

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Abstract

We apply a linearization technique for nonconvex quadratic problemswith box constraints. We show that cutting plane algorithms can bedesigned to solve the equivalent problems which minimize alinear function over a convex region. We propose several classes ofvalid inequalities of the convex region which are closely related tothe Boolean quadric polytope.We also describe heuristic procedures for generating cutting planes.Results of preliminary computational experimentsshow that our inequalities generate a polytope whichis a fairly tight approximation of the convex region.