Burer, S and Letchford, A N (2009) On non-convex quadratic programming with box constraints. SIAM Journal on Optimization, 20 (2). pp. 1073-1089.Full text not available from this repository.
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.
|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|
|Deposited On:||11 Jul 2011 19:29|
|Last Modified:||26 Jul 2012 19:14|
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