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

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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 \(\varepsilon \)-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.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments that helped me to improve the presentation of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Chongqing Normal University, Chongqing, 401331, China

    Hui Guo

  2. College of Sciences, Shanghai University, Shanghai, 200444, China

    Yan-Qin Bai

Authors
  1. Hui Guo
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  2. Yan-Qin Bai
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Corresponding author

Correspondence to Hui Guo.

Additional information

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).

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Guo, H., Bai, YQ. A Kind of Unified Strict Efficiency via Improvement Sets in Vector Optimization. J. Oper. Res. Soc. China 6, 557–569 (2018). https://doi.org/10.1007/s40305-017-0185-z

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  • DOI: https://doi.org/10.1007/s40305-017-0185-z

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