Journal of Global Optimization

, Volume 7, Issue 1, pp 1–31

A reformulation-convexification approach for solving nonconvex quadratic programming problems

Authors

  • Hanif D. Sherali
    • Department of Industrial and Systems Engineering Virginia Polytechnic Institute and State University Blacksburg
  • Cihan H. Tuncbilek
    • Department of Industrial and Systems Engineering Virginia Polytechnic Institute and State University Blacksburg
Article

DOI: 10.1007/BF01100203

Cite this article as:
Sherali, H.D. & Tuncbilek, C.H. J Glob Optim (1995) 7: 1. doi:10.1007/BF01100203

Abstract

In this paper, we consider the class of linearly constrained nonconvex quadratic programming problems, and present a new approach based on a novel Reformulation-Linearization/Convexification Technique. In this approach, a tight linear (or convex) programming relaxation, or outer-approximation to the convex envelope of the objective function over the constrained region, is constructed for the problem by generating new constraints through the process of employing suitable products of constraints and using variable redefinitions. Various such relaxations are considered and analyzed, including ones that retain some useful nonlinear relationships. Efficient solution techniques are then explored for solving these relaxations in order to derive lower and upper bounds on the problem, and appropriate branching/partitioning strategies are used in concert with these bounding techniques to derive a convergent algorithm. Computational results are presented on a set of test problems from the literature to demonstrate the efficiency of the approach. (One of these test problems had not previously been solved to optimality). It is shown that for many problems, the initial relaxation itself produces an optimal solution.

Key words

Quadratic programmingindefinite quadratic problemsreformulation-linearization techniquereformulation-convexification approachouter-approximationstight linear programming relaxations

Copyright information

© Kluwer Academic Publishers 1995