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Generalized semi-infinite optimization : a first order optimality condition and examples
Jongen, H.Th. (RWTH Aachen. Department of Mathematics)
Rückmann, J.-J. (University of Erlangen-Nürnberg. Institute of Applied Mathematics II)
Stein, O. (RWTH Aachen. Department of Mathematics)

Data: 1998
Resum: We consider a generalized semi-infinite optimization problem (GSIP) of the form (GSIP) min{f(x) $x (is in) M}, where M = {x (is in) R^nh_i(x) = 0, i = 1,. . . ,m, G(x, y) >= 0, y (is in) 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.
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: Generalized semi-infinite optimization problem ; First order necessary optimality condition ; Fritz John condition
Publicat a: Mathematical Programming, vol. 83 n. 1 (1998) p. 145-158, ISSN 0025-5610

14 p, 493.5 KB
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