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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)
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PDF [295 KB, uploaded 24 April 2019]

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. 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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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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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