Constraint qualification in a general class of Lipschitzian mathematical programming problems

The Kuhn-Tucker type necessary optimality conditions are given for the problem of minimizing the sum of a differentiable function and a locally Lipschitzian function subject to a set of differentiable nonlinear inequalities on a convex subset C of R-n, under the condition of a generalized Kuhn-Tucker constraint qualification or a generalized Arrow-Hurwicz-Uzawa constraint qualification. The case when the set C is open is shown to be a special one of our results, which helps us to improve some of the existing results in the literature. To finish we consider several test problems.