First order optimality conditions for generalized semi-infinite programming problems
نویسندگان
چکیده
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 takes a weaker form unless certain constraint qualification is satisfied. In the completely convex case where the objective of the lower level problem is concave and the constraint functions are quasiconvex, we show that the KKT condition takes a sharper form.
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