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Optimality conditions in global optimization and their applications

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Abstract

In this paper we derive necessary and sufficient conditions for some problems of global minimization. Our approach is based on methods of abstract convexity: we use a representation of an upper semicontinuous function as the lower envelope of a family of convex functions. We discuss applications of conditions obtained to the examination of some tractable sufficient conditions for the global minimum and to the theory of inequalities.

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Authors and Affiliations

  1. School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, 3353, VIC, Australia

    A. M. Rubinov & Z. Y. Wu

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  1. A. M. Rubinov
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  2. Z. Y. Wu
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Correspondence to Z. Y. Wu.

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The work was supported by a grant from the Australian Research Council.

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Rubinov, A.M., Wu, Z.Y. Optimality conditions in global optimization and their applications. Math. Program. 120, 101–123 (2009). https://doi.org/10.1007/s10107-007-0142-4

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  • DOI: https://doi.org/10.1007/s10107-007-0142-4

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