Mixed Type Duality for Set-valued Optimization Problems via Higher-order Radial Epiderivatives. (2nd July 2016)

• Record Type: Journal Article
• Authors: Anh, Nguyen Le Hoang
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 7(2016)
• Page Start: 823
• Page End: 838
• Publication Date: 2016-07-02
• Subjects: Higher-order radial epiderivative -- Mixed duality -- Optimality condition -- Set-valued optimization -- strict minimizer; 46G05 -- 49J52 -- 90C46; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1179202
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we introduce a notion of higher-order radial epiderivative for set-valued maps and study its properties. A generalized concept of higher-order strict minimizers in set-valued optimization is proposed as well. By virtue of the radial epiderivative, we establish a mixed dual problem, and then weak, strong, and converse duality theorems are obtained in dealing with generalized strict minimizers.