Constraint qualification in a general class of nondifferentiable mathematical programming problems

The Kuhn–Tucker type necessary optimality conditions are given for the problem of minimizing a local Lipschitzian function subject to a set of differentiable nonlinear inequalities on a convex subset CC of RnRn, under the conditions of the generalized Kuhn–Tucker constraint qualification or the generalized Arrow–Hurwicz–Uzawa constraint qualification. The case when the set CC 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. What’s more, the case when the object function is the sum of a differentiable function and a convex function is also the special case of our results. Finally, the case when the object function is the quotient of two Lipschitz functions is the special case of our results too.