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An efficient algorithm for range computation of polynomials using the Bernstein form

DSpace at IIT Bombay

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Title An efficient algorithm for range computation of polynomials using the Bernstein form
 
Creator RAY, S
NATARAJ, PSV
 
Subject global optimization
filled functions
bernstein polynomials
global optimization
interval analysis
polynomial optimization
range computation
 
Description We present a novel optimization algorithm for computing the ranges of multivariate polynomials using the Bernstein polynomial approach. The proposed algorithm incorporates four accelerating devices, namely the cut-off test, the simplified vertex test, the monotonicity test, and the concavity test, and also possess many new features, such as, the generalized matrix method for Bernstein coefficient computation, a new subdivision direction selection rule and a new subdivision point selection rule. The features and capabilities of the proposed algorithm are compared with those of other optimization techniques: interval global optimization, the filled function method, a global optimization method for imprecise problems, and a hybrid approach combining simulated annealing, tabu search and a descent method. The superiority of the proposed method over the latter methods is illustrated by numerical experiments and qualitative comparisons.
 
Publisher SPRINGER
 
Date 2011-08-29T09:15:22Z
2011-12-26T12:58:31Z
2011-12-27T05:48:37Z
2011-08-29T09:15:22Z
2011-12-26T12:58:31Z
2011-12-27T05:48:37Z
2009
 
Type Article
 
Identifier JOURNAL OF GLOBAL OPTIMIZATION, 45(3), 403-426
0925-5001
http://dx.doi.org/10.1007/s10898-008-9382-y
http://dspace.library.iitb.ac.in/xmlui/handle/10054/12039
http://hdl.handle.net/10054/12039
 
Language en