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New higher-order strong Karush-Kuhn-Tucker conditions for proper solutions in nonsmooth optimization. (English) Zbl 1464.90093

Higher-order necessary conditions for positively efficient solutions in the senses of Henig and Benson as well as of linear scalarization (called here positively properly efficient) to set-valued optimization problems are provided. Additionally employing certain regularity conditions they turn into the Karush-Kuhn-Tucker type formulae. Several existing results in the literature are thus improved or generalized, in particular even some in vector optimization.

MSC:

90C29 Multi-objective and goal programming
49J52 Nonsmooth analysis
90C46 Optimality conditions and duality in mathematical programming
90C48 Programming in abstract spaces
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