Some Applications of a Polynomial Inequality to Global Optimization

J. F. Zhang and C. P. Kwong
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J. F. Zhang: Chinese University of Hong Kong
C. P. Kwong: Chinese University of Hong Kong

Journal of Optimization Theory and Applications, 2005, vol. 127, issue 1, No 11, 193-205

Abstract: Abstract In this paper, we use the Ehlich-Zeller-Gärtel inequality to derive an algorithm for finding the global minima of polynomials over hyperrectangles as well as to provide a bounding method for the branch-and-bound algorithm. The latter application of the inequality results in an improved algorithm which gives simultaneously a decreasing upper bound and an increasing lower bound for the global minimum at each iteration. The algorithm can be used also to find the Lipschitz constant of a polynomial.

Keywords: Ehlich-Zeller-Gärtel inequality; Lipschitz optimization; branch-and-bound algorithms; polynomials (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-005-6400-9

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