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

  • Authors:

  • Shashwati Ray;P. S. Nataraj

  • Affiliations:

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

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2009

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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.