Copyright © 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.
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.