An efficient algorithm for range computation of polynomials using the Bernstein form |
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Authors: | Shashwati Ray P. S. V. Nataraj |
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Affiliation: | (1) School of Mathematics and Computer Science, Chongqing Normal University, Chongqing, 400047, China;(2) Department of Applied Mathematics, The Hong Kong Polytechnic University, Kongloon, Hong Kong, China;(3) Department of Mathematics, Shanghai University, Shanghai, 200444, China;(4) Present address: School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, VIC, 3353, Australia |
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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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