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- Title
New results on semidefinite bounds for ℓ1-constrained nonconvex quadratic optimization.
- Authors
Xia, Yong
- Abstract
In this paper, we show that the direct semidefinite programming (SDP) bound for the nonconvex quadratic optimization problem over ℓ1 unit ball (QPL1) is equivalent to the optimal d.c. (difference between convex) bound for the standard quadratic programming reformulation of QPL1. Then we disprove a conjecture about the tightness of the direct SDP bound. Finally, as an extension of QPL1, we study the relaxation problem of the sparse principal component analysis, denoted by QPL2L1. We show that the existing direct SDP bound for QPL2L1 is equivalent to the doubly nonnegative relaxation for variable-splitting reformulation of QPL2L1.
- Subjects
SEMIDEFINITE programming; MATHEMATICAL bounds; NONCONVEX programming; QUADRATIC programming; MATHEMATICAL optimization; RELAXATION methods (Mathematics)
- Publication
RAIRO -- Operations Research, 2013, Vol 47, Issue 3, p285
- ISSN
0399-0559
- Publication type
Article
- DOI
10.1051/ro/2013039