Please use this identifier to cite or link to this item: http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/169
Title: Global optimality principles for polynomial optimization over box or bivalent constraints by separable polynomial approximations
Authors: Jeyakumar, V
Li, G
Srisatkunarajah, S
Keywords: Bivalent constraints;Box constraints;Global optimality conditions;Global optimization;Polynomial optimization
Issue Date: 2013
Publisher: Springer Science+Business Media New York
Abstract: In this paper we present necessary conditions for global optimality for polynomial problems with box or bivalent constraints using separable polynomial relaxations. We achieve this by first deriving a numerically checkable characterization of global optimality for separable polynomial problems with box as well as bivalent constraints. Our necessary optimality conditions can be numerically checked by solving semi-definite programming problems. Then, by employing separable polynomial under-estimators, we establish sufficient conditions for global optimality for classes of polynomial optimization problems with box or bivalent constraints. We construct underestimators using the sum of squares convex (SOS-convex) polynomials of real algebraic geometry. An important feature of SOS-convexity that is generally not shared by the standard convexity is that whether a polynomial is SOS-convex or not can be checked by solving a semidefinite programming problem. We illustrate the versatility of our optimality conditions by simple numerical examples.
URI: http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/169
ISSN: 09255001
Appears in Collections:Mathematics and Statistics



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