Journal
OPERATIONS RESEARCH LETTERS
Volume 42, Issue 1, Pages 34-40Publisher
ELSEVIER
DOI: 10.1016/j.orl.2013.11.005
Keywords
Convex polynomial optimization; Sums-of-squares of polynomials; Semidefinite programming
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Funding
- Australian Research Council
- Vietnam National Foundation for Science and Technology Development (NAFOSTED) [101.04-2013.07]
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We show that the Lasserre hierarchy of semidefinite programming (SDP) relaxations with a slightly extended quadratic module for convex polynomial optimization problems always converges asymptotically even in the case of non-compact semi-algebraic feasible sets. We then prove that the positive definiteness of the Hessian of the associated Lagrangian at a saddle-point guarantees the finite convergence of the hierarchy. We do this by establishing a new sum-of-squares polynomial representation of convex polynomials over convex semi-algebraic sets. (C) 2013 Elsevier B.V. All rights reserved.
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