Optimality Conditions for Approximate Solutions of Set Optimization Problems with the Minkowski Difference
Author:
Zhang Yuhe1ORCID,
Wang Qilin1
Affiliation:
1. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China
Abstract
In this paper, we study the optimality conditions for set optimization problems with set criterion. Firstly, we establish a few important properties of the Minkowski difference for sets. Then, we introduce the generalized second-order lower radial epiderivative for a set-valued maps by Minkowski difference, and discuss some of its properties. Finally, by virtue of the generalized second-order lower radial epiderivatives and the generalized second-order radial epiderivatives, we establish the necessary optimality conditions and sufficient optimality conditions of approximate Benson proper efficient solutions and approximate weakly minimal solutions of unconstrained set optimization problems without convexity conditions, respectively. Some examples are provided to illustrate the main results obtained.
Funder
National Natural Science Foundation of China
Group Building Project for Scientifc Innovation for Universities in Chongqing
Science and technology research project of Chongqing Municipality Education Commission
Joint Training Base Construction Project for Graduate Students in Chongqing
Graduate Student Science and Technology Innovation Project of Chongqing Jiaotong University
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference28 articles.
1. Set-valued optimization in welfare economies;Bao;Adv. Math. Econ.,2011
2. Order relations of sets and its application in social-economics;Neukel;J. Appl. Math. Sci.,2013
3. Characterizations of multiobjective robustness via oriented distance function and image space analysis;Ansari;J. Optim. Theory Appl.,2019
4. Necessary and sufficient conditions for set-valued maps with set optimization;Abdessamad;J. Abstr. Appl. Anal.,2018
5. Optimality conditions for set optimization using a directional derivative based on generalized Steiner sets;Baier;Optimization,2022