A general Farkas lemma and characterization of optimality for a nonsmooth program involving convex processes (Q1821698)

In this paper, a generalization of the Farkas lemma is presented for nonlinear mappings which involve a convex process and a generalized convex function. Using this result, a complete characterization of optimality is obtained for the following nonsmooth programming problem: minimize f(x), subject to -b\(\in H(x)\), where f is a locally Lipschitz function satisfying a generalized convexity hypothesis and H is a closed convex process.