Journal of Applied Mathematics

Higher-Order Weakly Generalized Epiderivatives and Applications to Optimality Conditions

Qilin Wang and Guolin Yu

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 691018, 19 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495152

Digital Object Identifier
doi:10.1155/2012/691018

Mathematical Reviews number (MathSciNet)
MR2927271

Zentralblatt MATH identifier
1245.49030

Citation

Wang, Qilin; Yu, Guolin. Higher-Order Weakly Generalized Epiderivatives and Applications to Optimality Conditions. J. Appl. Math. 2012 (2012), Article ID 691018, 19 pages. doi:10.1155/2012/691018. https://projecteuclid.org/euclid.jam/1355495152


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