A reformulationconvexification approach for solving nonconvex quadratic programming problems
 Hanif D. Sherali,
 Cihan H. Tuncbilek
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In this paper, we consider the class of linearly constrained nonconvex quadratic programming problems, and present a new approach based on a novel ReformulationLinearization/Convexification Technique. In this approach, a tight linear (or convex) programming relaxation, or outerapproximation 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.
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 Title
 A reformulationconvexification approach for solving nonconvex quadratic programming problems
 Journal

Journal of Global Optimization
Volume 7, Issue 1 , pp 131
 Cover Date
 19950701
 DOI
 10.1007/BF01100203
 Print ISSN
 09255001
 Online ISSN
 15732916
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Quadratic programming
 indefinite quadratic problems
 reformulationlinearization technique
 reformulationconvexification approach
 outerapproximations
 tight linear programming relaxations
 Industry Sectors
 Authors

 Hanif D. Sherali ^{(1)}
 Cihan H. Tuncbilek ^{(1)}
 Author Affiliations

 1. Department of Industrial and Systems Engineering Virginia Polytechnic Institute and State University Blacksburg, 240610118, Virginia, USA