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

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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.

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Authors and Affiliations

  1. Systems and Control Engineering Group, ACRE Building, Indian Institute of Technology, Bombay, 400 076, India

    Shashwati Ray & P. S. V. Nataraj

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  1. Shashwati Ray
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  2. P. S. V. Nataraj
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Correspondence to P. S. V. Nataraj.

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Ray, S., Nataraj, P.S.V. An efficient algorithm for range computation of polynomials using the Bernstein form. J Glob Optim 45, 403–426 (2009). https://doi.org/10.1007/s10898-008-9382-y

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