Open Access

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

Fixed Point Theory and Applications20102011:175327

Received: 4 January 2010

Accepted: 6 December 2010

Published: 29 December 2010


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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Authors’ Affiliations

Department of Applied Mathematics, Pukyong National University
Department of Natural Sciences, Nhatrang College of Education


© D. S. Kim and T. Q. Son. 2011

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.