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Necessary optimality conditions for nonsmooth generalized semi-infinite programming problems. (English) Zbl 1188.90261
Summary: This paper is devoted to the study of nonsmooth generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be locally Lipschitz. We introduce a constraint qualification which is based on the Mordukhovich subdifferential. Then, we derive a Fritz-John type necessary optimality condition. Finally, interrelations between the new and the existing constraint qualifications such as the Mangasarian-Fromovitz, linear independent, and the Slater are investigated.
MSC:
90C34Semi-infinite programming
90C40Markov and semi-Markov decision processes
49J52Nonsmooth analysis (other weak concepts of optimality)