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On the Mangasarian-Fromovitz constraint qualification and Karush-Kuhn-Tucker conditions in nonsmooth semi-infinite multiobjective programming. (English) Zbl 1517.90134

The authors consider nonsmooth semi-infinite multi-objective programming problems. The Michel-Penot directional derivative and the Studniarski derivative of order \(p\) are used in order to derive a Manganarian-Fromovitz-type constraint qualification. Further, KKT optimality conditions for Borwein-proper and firm solutions are obtained combining the qualification condition with the Pshenichnyi-Levitin-Valadire property. Comparisons to other qualification conditions are provided as well as applications to semi-infinite multi-objective fractional problems and minimax problems.

MSC:

90C29 Multi-objective and goal programming
90C34 Semi-infinite programming
90C46 Optimality conditions and duality in mathematical programming
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