Constraint qualifications in a class of nondifferentiable mathematical programming problems

Abstract

The Kuhn–Tucker type necessary optimality conditions are given for the problem of minimizing the sum of a differentiable function and a convex function subject to a set of differentiable nonlinear inequalities on a convex subset C of R n , under the conditions similar to the Kuhn–Tucker constraint qualification or the Arrow–Hurwicz–Uzawa constraint qualification. The case when the set C is open (not necessarily convex) is shown to be a special one of our results, which helps us to improve some of the existing results in the literature.