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.
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This work was supported by the Research Grants Council of Hong Kong, Project ID 2050277. The authors are grateful to Professor B. Tibken and Mr. K.F. Dilaver for their provision of an English version of Gärtel’s proof of the EZG inequality, to an anonymous referee for valuable comments, and to Miss Dandan Li and Dr. Mark S.K. Lau for their help in the preparation of this paper.
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Zhang, J.F., Kwong, C.P. Some Applications of a Polynomial Inequality to Global Optimization. J Optim Theory Appl 127, 193–205 (2005). https://doi.org/10.1007/s10957-005-6400-9
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DOI: https://doi.org/10.1007/s10957-005-6400-9