Generalized Higher-Order Optimality Conditions for Set-Valued Optimization under Henig Efficiency |
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| Authors: | Q L Wang S J Li |
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| Institution: | 1. College of Mathematics and Science , Chongqing University , Chongqing, China;2. College of Sciences , Chongqing Jiaotong University , Chongqing, China Wangql97@126.com;4. College of Mathematics and Science , Chongqing University , Chongqing, China |
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| Abstract: | In this paper, generalized mth-order contingent epiderivative and generalized mth-order epiderivative of set-valued maps are introduced, respectively. By virtue of the generalized mth-order epiderivatives, generalized necessary and sufficient optimality conditions are obtained for Henig efficient solutions to a set-valued optimization problem whose constraint set is determined by a fixed set. Generalized Kuhn–Tucker type necessary and sufficient optimality conditions are also obtained for Henig efficient solutions to a set-valued optimization problem whose constraint set is determined by a set-valued map. |
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| Keywords: | Generalized higher-order optimality conditions Generalized mth-order contingent (adjacent) epiderivative Henig efficient solutions Set-valued optimization |
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