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. ISSN 1095-7189

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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:
Journal Article
Journal or Publication Title:
SIAM Journal on Optimization
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/aacsb/disciplinebasedresearch
Subjects:
ID Code:
45296
Deposited By:
Deposited On:
11 Jul 2011 18:29
Refereed?:
Yes
Published?:
Published
Last Modified:
03 Mar 2020 08:22