Continuous Optimization

A Kind of Unified Strict Efficiency via Improvement Sets in Vector Optimization

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  • 1 Department of Mathematics, Chongqing Normal University, Chongqing 401331, China
    2 College of Sciences, Shanghai University, Shanghai 200444, China

Online published: 2018-12-30

Supported by

This research was supported by the National Natural Science Foundation of China (No. 11671062), the Chongqing Municipal Education Commission (No. KJ1500310), the Doctor startup fund of Chongqing Normal University (No. 16XLB010).

Abstract

In this paper, we propose a kind of unified strict efficiency named E-strict efficiency via improvement sets for vector optimization. This kind of efficiency is shown to be an extension of the classical strict efficiency and -strict efficiency and has many desirable properties. We also discuss some relationships with other properly efficiency based on improvement sets and establish the corresponding scalarization theorems by a base-functional and a nonlinear functional. Moreover, some examples are given to illustrate the main conclusions.

Cite this article

Hui Guo, Yan-Qin Bai . A Kind of Unified Strict Efficiency via Improvement Sets in Vector Optimization[J]. Journal of the Operations Research Society of China, 2018 , 6(4) : 557 -570 . DOI: https://doi.org/10.1007/s40305-017-0185-z

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