Higher-Order Weakly Generalized Epiderivatives and Applications to Optimality Conditions. (30th May 2012)

• Record Type: Journal Article
• Authors: Wang, Qilin; Yu, Guolin
• Other Names: Conca C. Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2012(2012)
• Publication Date: 2012-05-30
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2012/691018
• Languages: English
• ISSNs: 1110-757X

Abstract

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.