Generalized semi-infinite optimization: A first order optimality condition and examples

We consider a generalized semi-infinite optimization problem (GSIP) of the form (GSIP) min{f(x) Ix E M}, where M = {x E N"lhi(x ) = 0, i = 1,...,m, G(x,y) /> 0, y E Y(x)} and all appearing functions are continuously differentiable. Furthermore, we assume that the set Y(x) is compact for all x under consideration and the set-valued mapping Y(.) is upper semi-continuous. The difference with a standard semi-infinite problem lies in the x-dependence of the index set Y. We prove a first order necessary optimality condition of Fritz John type without assuming a constraint qualification or any kind of reduction approach. Moreover, we discuss some geometrical properties of the feasible set M. 9 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

• Type: Journal
• Year: 1998
• Where: MP
• Authors: Hubertus Th. Jongen, Jan-J. Rückmann, Oliver Stein
• Keywords: Generalized Semi-infinite Optimization, MP 1998, Order Necessary Optimality, Standard Semi-infinite Problem