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Open AccessArticle

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

1
College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China
2
Center for Fundamental Science; and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80708, Taiwan
3
Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 80708, Taiwan
*
Authors to whom correspondence should be addressed.
Current address: No.66 Xuefu Rd., Nan’an Dist., Chongqing 400074, China.
Mathematics 2019, 7(4), 372; https://doi.org/10.3390/math7040372
Received: 9 March 2019 / Revised: 17 April 2019 / Accepted: 17 April 2019 / Published: 24 April 2019
(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)
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. View Full-Text
Keywords: set-valued optimization problems; higher-order weak adjacent epiderivatives; higher-order mond-weir type dual; benson proper efficiency set-valued optimization problems; higher-order weak adjacent epiderivatives; higher-order mond-weir type dual; benson proper efficiency
MDPI and ACS Style

He, L.; Wang, Q.-L.; Wen, C.-F.; Zhang, X.-Y.; Li, X.-B. A Kind of New Higher-Order Mond-Weir Type Duality for Set-Valued Optimization Problems. Mathematics 2019, 7, 372.

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