Abstract
This paper is devoted to the study of optimality conditions and duality theory for a set-valued optimization problem. by using the higher-order radial derivative of a set-valued map, we establish Fritz John and Kuhn-Tucker types necessary and sufficient optimality conditions for a weak minimizer of a set-valued optimization problem under the assumption that set-valued maps in the formulation of objective and constraint maps are near cone-subconvexlike. As an application of the optimality conditions, we prove weak, strong and converse duality theorems for Mond-Weir and Wolfe types dual problems.
Highlights
In recent years, there has been an increasing interest in the investigation of higher-order derivatives, higher-order optimality conditions and duality theory for set-valued optimization problems
Higherorder derivatives in the related literatures can be divided into two categories: First, the existences of higherorder derivatives depend on the choice of lower-order directions, for instance, higher-oder contingent derivatives [1], the generalized higher-order contingent derivatives [2], cone-directed higher-order contingent derivatives [3], higher-order generalized contingent epiderivatives [4], higher-order weak epiderivatives [5], and variational sets [6, 7, 8], etc.; Second, the direction of higher-order derivatives does not depend on lower-order direction, for example, Higher-order Studniarski derivative [9, 10, 11] enjoys this advantage
Much attention has been paid upon optimality conditions and related topics for vector optimization by using Studniarski derivatives [9, 10, 11, 12, 13]
Summary
There has been an increasing interest in the investigation of higher-order (generalized) derivatives, higher-order optimality conditions and duality theory for set-valued optimization problems. [18] made a higher-order extensions for radial derivatives and presented optimality conditions in type of separating of sets for several kinds of efficiency in set-valued optimization. Based upon the above observations, this paper is focused on higher-order radial derivatives of set-valued maps and weak minimizer of a set-valued optimization problem under weaker condition on convexity. The purpose of this paper is two folds: first, we establish the optimality conditions for weak minimizers in Fritz John and KuhnTucker types; second, we provide an employment of optimality conditions for weak minimizers to obtain some duality results for higher-order Mond-Weir and Wolfe types dual problems.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Statistics, Optimization & Information Computing
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
