Second Order Conditions in Nonlinear Nonsmooth Problems of Semi-Infinite Programming

Abstract

The problem we shall consider is stated as follows: (SIP) minimize $$ f(x) = \mathop{{\max }}\limits_{{s \in S}} \,f(s,x) $$ subject to $$ F(x) = 0; $$ x takes values in Rn (the n-dimensional linear space with some fixed, say, Euclidean norm), S is a compact Hausdorff space, f(s,x) is a function on S x Rn and F: Rn→Rm.