A Kind of New Higher-Order Mond-Weir Type Duality for Set-Valued Optimization Problems

Liu He, Qi-Lin Wang, Ching-Feng Wen, Xiao-Yan Zhang and Xiao-Bing Li
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Liu He: College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China
Qi-Lin Wang: College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China
Ching-Feng Wen: Center for Fundamental Science; and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80708, Taiwan
Xiao-Yan Zhang: College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China
Xiao-Bing Li: College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China

Mathematics, 2019, vol. 7, issue 4, 1-18

Abstract: In this paper, we introduce the notion of higher-order weak adjacent epiderivative for a set-valued map without lower-order approximating directions and obtain existence theorem and some properties of the epiderivative. Then by virtue of the epiderivative and Benson proper efficiency, we establish the higher-order Mond-Weir type dual problem for a set-valued optimization problem and obtain the corresponding weak duality, strong duality and converse duality theorems, respectively.

Keywords: set-valued optimization problems; higher-order weak adjacent epiderivatives; higher-order mond-weir type dual; benson proper efficiency (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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