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Characterizations of improvement sets via quasi interior and applications in vector optimization

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Abstract

In this paper, we first give some characterizations of improvement sets via quasi interior. Furthermore, as applications of these characterizations, we establish an alternative theorem via improvement sets and quasi interior, and then obtain a scalarization result of weak \(E\)-efficient solutions defined by improvement sets and quasi interior for vector optimization problems with set-valued maps. Moreover, we also present some examples to illustrate the main conditions and results.

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Acknowledgments

This research was partially supported by the National Natural Science Foundation of China (Grants 11431004, 11271391, 11301574), the Second Sponsoring Plan for Young Key Teachers from Universities of Chongqing and the Graduate Students Scientific Research Innovation Project of Chongqing. The authors thank Professor Xin Min Yang for his valuable comments on the original version of this article. The authors also thank anonymous reviewers for their valuable comments and suggestions which have improved the presentation of the paper.

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The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. College of Mathematics Science, Chongqing Normal University, Chongqing, 401331, China

    Yuan Mei Xia, Wan Li Zhang & Ke Quan Zhao

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  1. Yuan Mei Xia
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  2. Wan Li Zhang
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  3. Ke Quan Zhao
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Correspondence to Ke Quan Zhao.

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Xia, Y.M., Zhang, W.L. & Zhao, K.Q. Characterizations of improvement sets via quasi interior and applications in vector optimization. Optim Lett 10, 769–780 (2016). https://doi.org/10.1007/s11590-015-0897-0

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