An Optimality Conditione for Locally Lipschitz semi-infinite Problems

This paper is devoted to the study of locally Lipschitz semi-infinite programming problems in which the index set of the inequality constraints is assumed to be arbitrary. We introduce an analogous of the Arrow-Hurwitcz-Uzawa constraint qualification which is based on the Clarke subdifferential. Then, we derive a Karush-Kuhn-Tucker type necessary condition . Finally, interrelations between the new and the Slater constraint qualifications are investigated.