In this paper we study first order optimality conditions for the class of generalized semi-infinite programming problems (GSIPs). We extend various wellknown constraint qualifications for finite programming problems to GSIPs and analyze the extent to which a corresponding Karush-Kuhn-Tucker (KKT) condition depends on these extensions. It is shown that in general the KKT condition for GSIPs take...

In this paper, we study a class of fractional semi-infinite polynomial programming (FSIPP) problems, in which the objective is fraction convex and concave polynomial, constraints consist infinitely many inequalities. To solve such problem, first reformulate it to pair primal dual conic optimization reduce semidefinite (SDP) problems if can bring sum-of-squares structures into constraints. end, ...

Approximate optimality conditions for a class of nonconvex semi-infinite programs involving support functions are given. The objective function and the constraint functions are locally Lipschitz functions on n . By using a Karush-Kuhn-Tucker KKT condition, we deduce a necessary optimality condition for local approximate solutions. Then, generalized KKT conditions for the problems are proposed. ...