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Improved Lipschitz bounds with the first norm for function values over multidimensional simplex

    Remigijus Paulavičius Affiliation
    ; Julius Žilinskas Affiliation

Abstract

A branch and bound algorithm for global optimization is proposed, where the maximum of an upper bounding function based on Lipschitz condition and the first norm over a simplex is used as the upper bound of function. In this case the graph of bounding function is intersection of n‐dimensional pyramids and its maximum point is found solving a system of linear equations. The efficiency of the proposed global optimization algorithm is evaluated experimentally.


First Published Online: 14 Oct 2010

Keyword : global optimization, branch and bound algorithms, Lipschitz optimization, the first norm

How to Cite
Paulavičius, R., & Žilinskas, J. (2008). Improved Lipschitz bounds with the first norm for function values over multidimensional simplex. Mathematical Modelling and Analysis, 13(4), 553-563. https://doi.org/10.3846/1392-6292.2008.13.553-563
Published in Issue
Dec 31, 2008
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