On quasi approximate solutions for nonsmooth robust semi-infinite optimization problems

This paper devotes to the quasi -solution for robust semi-infinite optimization problems (RSIP) involving a locally Lipschitz objective function and infinitely many locally Lipschitz constraint functions with data uncertainty. Under the fulfillment of robust type Guignard constraint qualification and robust type Kuhn-Tucker constraint qualification, a necessary condition for a quasi -solution to problem (RSIP). After introducing the generalized convexity, we give a sufficient optimality for such a quasi -solution to problem (RSIP). Finally, we also establish approximate duality theorems in term of Wolfe type which is formulated in approximate form.