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-Optimal Solutions in Nonconvex Semi-Infinite Programs with Support Functions

Abstract

Approximate optimality conditions for a class of nonconvex semi-infinite programs involving support functions are given. The objective function and the constraint functions are locally Lipschitz functions on . By using a Karush-Kuhn-Tucker (KKT) condition, we deduce a necessary optimality condition for local approximate solutions. Then, generalized KKT conditions for the problems are proposed. Based on properties of -semiconvexity and semiconvexity applied to locally Lipschitz functions and generalized KKT conditions, we establish sufficient optimality conditions for another kind of local approximate solutions of the problems. Obtained results in case of nonconvex semi-infinite programs and nonconvex infinite programs are discussed.

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Correspondence to DoSang Kim.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Kim, D., Son, T. -Optimal Solutions in Nonconvex Semi-Infinite Programs with Support Functions. Fixed Point Theory Appl 2011, 175327 (2011). https://doi.org/10.1155/2011/175327

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Keywords

  • Differential Geometry
  • Computational Biology
  • Full Article
  • Publisher Note