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 |
Files in This Item:
File | Description | Size | Format | |
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2.Global optimality principles for polynomial optimization over box or bivalent constraints by separable polynomial approximations-Jeyakumar.pdf | 175.62 kB | Adobe PDF | View/Open |
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