Strong duality with super efficiency in set-valued optimization

Volume 10, Issue 6, pp 3261--3272 http://dx.doi.org/10.22436/jnsa.010.06.37

Publication Date: June 25, 2017 Submission Date: March 06, 2017

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Authors

Guolin Yu - Institute of Applied Mathematics, North Minzu University, Yinchuan, Ningxia 750021, P. R. China.

Abstract

This paper is devoted to the study of four dual problems of a primal vector optimization problem involving nearly subconvexlike set-valued mappings. For each dual problem, a strong duality theorem with super efficiency is established. The strong duality result can be expressed as follows: starting from a super minimizer of the primal problem, a super maximizer of the dual problem can be constructed such that the corresponding objective values of both problems are equal. The results improve the corresponding ones in the literature.

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Keywords

• Super efficiency
• Henig proper efficiency
• nearly subconvexlike set-valued mappings
• set-valued optimization
• strong duality.

MSC

•  90C29
•  90C46
•  26B25

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