Journal
OPERATIONS RESEARCH LETTERS
Volume 40, Issue 6, Pages 529-536Publisher
ELSEVIER
DOI: 10.1016/j.orl.2012.09.006
Keywords
Polynomial optimization; Convex semi-definite programming; SOS-convex polynomials; Sum of squares polynomials; Fractional programs
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Funding
- Australian Research Council
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This paper addresses the issue of which nonlinear semidefinite linear programming problems possess exact semidefinite linear programming (SDP) relaxations under a constraint qualification. We establish exact SDP relaxations for classes of nonlinear semidefinite programming problems with SOS-convex polynomials. These classes include SOS-convex semidefinite programming problems and fractional semidefinite programming problems with SOS-convex polynomials. The class of SOS-convex polynomials contains convex quadratic functions and separable convex polynomials. We also derive numerically checkable conditions, completely characterizing minimizers of these classes of problems. (C) 2012 Elsevier B.V. All rights reserved.
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