‎Necessary Conditions in Generalized Semi-Infinite Optimization with Nondifferentiable Convex Data

Abstract: In this paper we focus on generalized semi-infnite optimization problem in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be convex, not necessarily differentiable. We introduce three constraint qualifcations which are based on the convex subdifferential, and derive some Kuhn-Tucker type necessary optimality conditions for the problem.