Journal of Global Optimization

, Volume 13, Issue 2, pp 151–170

A Polyhedral Approach for Nonconvex Quadratic Programming Problems with Box Constraints

  • Yasutoshi Yajima
  • Tetsuya Fujie

DOI: 10.1023/A:1008293029350

Cite this article as:
Yajima, Y. & Fujie, T. Journal of Global Optimization (1998) 13: 151. doi:10.1023/A:1008293029350


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 methodLinearization techniqueNonconvex quadratic programsValid inequalities

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Yasutoshi Yajima
    • 1
  • Tetsuya Fujie
    • 2
  1. 1.Department of Industrial Engineering and ManagementTokyo Institute of TechnologyOh-Okayama, Meguro-ku, TokyoJapan (e-mail: Email
  2. 2.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyOh-Okayama, Meguro-ku, TokyoJapan