This article is part of the series Equilibrium Problems and Fixed Point Theory.

Open Access Research Article

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

DoSang Kim1* and TaQuang Son2

Author Affiliations

1 Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea

2 Department of Natural Sciences, Nhatrang College of Education, 1 Nguyen Chanh, Nhatrang, Vietnam

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Fixed Point Theory and Applications 2011, 2011:175327 doi:10.1155/2011/175327


The electronic version of this article is the complete one and can be found online at: http://www.fixedpointtheoryandapplications.com/content/2011/1/175327


Received:6 December 2010
Accepted:29 December 2010
Published:4 January 2010

© 2011 Do Sang Kim and Ta Quang Son.

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.

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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