Journal of the Operations Research Society of China ›› 2018, Vol. 6 ›› Issue (4): 557-570.doi: https://doi.org/10.1007/s40305-017-0185-z

Special Issue: Vector and tensor optimization

• Continuous Optimization • Previous Articles     Next Articles

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

Hui Guo1 · Yan-Qin Bai2   

  1. 1 Department of Mathematics, Chongqing Normal University, Chongqing 401331, China
    2 College of Sciences, Shanghai University, Shanghai 200444, China
  • Online:2018-12-30 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).

PDF

72

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.

Key words: E-strict efficiency ·, Improvement sets ·, Linear scalarization ·, Nonlinear scalarization ·, Vector optimization

Copyright © Operations Research Society of China, The Periodicals Agency of Shanghai University , and Springer-Verlag Berlin Heidelberg 2016