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Title: An efficient algorithm for range computation of polynomials using the Bernstein form
Authors: RAY, S
Keywords: Global Optimization
Filled Functions
Issue Date: 2009
Publisher: SPRINGER
Citation: JOURNAL OF GLOBAL OPTIMIZATION, 45(3), 403-426
Abstract: 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.
ISSN: 0925-5001
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