A Polyhedral Approach for Nonconvex Quadratic Programming Problems with Box Constraints

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 regio...

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Bibliographic Details
Published inJournal of global optimization Vol. 13; no. 2; p. 151
Main Authors Yajima, Yasutoshi, Fujie, Tetsuya
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.09.1998
Subjects
Algorithms
Approximation
Boolean
Integer programming
Linear programming
Quadratic programming
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Summary: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.
ISSN:0925-5001
1573-2916
DOI:10.1023/A:1008293029350