Higher-order optimality conditions for set-valued optimization with ordering cones having empty interior using variational sets
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In this paper, we first establish chain rules and sum rules for variational sets of type 2. For their applications, optimality conditions of two particular optimization problems are discussed. Then, we obtain higher-order optimality conditions for proper Henig solutions of a set-valued optimization problem in terms of variational sets of type 2 when ordering cones have empty interior.
KeywordsSet-valued optimization Higher-order optimality conditions Calculus rules Proper Henig solutions Variational sets Nearly subconvexlikeness
Mathematics Subject Classification32F17 46G05 54C60 90C46
This study was supported by the project of the Moravian-Silesian Region, Czech Republic Reg. No. 02692/2014/RRC. The author is grateful to an anonymous referee for his valuable comments which helped to improve the previous manuscript.
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