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On non-convex quadratic programming with box constraints

Burer, S and Letchford, A N (2009) On non-convex quadratic programming with box constraints. SIAM Journal on Optimization, 20 (2). pp. 1073-1089.

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Abstract

Nonconvex quadratic programming with box constraints is a fundamental NP-hard global optimization problem. Recently, some authors have studied a certain family of convex sets associated with this problem. We prove several fundamental results concerned with these convex sets: we determine their dimension, characterize their extreme points and vertices, show their invariance under certain affine transformations, and show that various linear inequalities induce facets. We also show that the sets are closely related to the Boolean quadric polytope, a fundamental polytope in the field of polyhedral combinatorics. Finally, we give a classification of valid inequalities and show that this yields a finite recursive procedure to check the validity of any proposed inequality.

Item Type: Article
Journal or Publication Title: SIAM Journal on Optimization
Uncontrolled Keywords: non-convex quadratic programming ; global optimisation ; polyhedral combinatorics ; convex analysis
Subjects: H Social Sciences > HB Economic Theory
Departments: Lancaster University Management School > Management Science
ID Code: 45296
Deposited By: ep_importer_pure
Deposited On: 11 Jul 2011 19:29
Refereed?: Yes
Published?: Published
Last Modified: 09 Apr 2014 22:30
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/45296

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