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2012 Higher-Order Weakly Generalized Epiderivatives and Applications to Optimality Conditions
Qilin Wang, Guolin Yu
J. Appl. Math. 2012: 1-19 (2012). DOI: 10.1155/2012/691018


The notions of higher-order weakly generalized contingent epiderivative and higher-order weakly generalized adjacent epiderivative for set-valued maps are proposed. By virtue of the higher-order weakly generalized contingent (adjacent) epiderivatives, both necessary and sufficient optimality conditions are obtained for Henig efficient solutions to a set-valued optimization problem whose constraint set is determined by a set-valued map. The imposed assumptions are relaxed in comparison with those of recent results in the literature. Examples are provided to show some advantages of our notions and results.


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Qilin Wang. Guolin Yu. "Higher-Order Weakly Generalized Epiderivatives and Applications to Optimality Conditions." J. Appl. Math. 2012 1 - 19, 2012.


Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1245.49030
MathSciNet: MR2927271
Digital Object Identifier: 10.1155/2012/691018

Rights: Copyright © 2012 Hindawi

Vol.2012 • 2012
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