期刊
SIAM JOURNAL ON OPTIMIZATION
卷 20, 期 2, 页码 1073-1089出版社
SIAM PUBLICATIONS
DOI: 10.1137/080729529
关键词
nonconvex quadratic programming; global optimization; polyhedral combinatorics; convex analysis
资金
- National Science Foundation [CCF-0545514]
- Engineering and Physical Sciences Research Council [EP/D072662/1]
- EPSRC [EP/F033613/1, EP/D072662/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/D072662/1, EP/F033613/1] Funding Source: researchfish
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 a. ne 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.
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