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Generalized semi-infinite optimization: A first order optimality condition and examples. (English) Zbl 0949.90090

Summary: We consider a Generalized Semi-Infinite Optimization Problem (GSIP) of the form

min{f(x)xM}( GSIP )

where M={x n h i (x)=0, i=1,,m, G(x,y)0, yY(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.


MSC:
90C34Semi-infinite programming
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