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Connectedness of Solution Sets for Weak Generalized Symmetric Ky Fan Inequality Problems via Addition-Invariant Sets

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Abstract

In this paper, the connectedness and path-connectedness of solution sets for weak generalized symmetric Ky Fan inequality problems with respect to addition-invariant set are studied. A class of weak generalized symmetric Ky Fan inequality problems via addition-invariant set is proposed. By using a nonconvex separation theorem, the equivalence between the solutions set for the symmetric Ky Fan inequality problem and the union of solution sets for scalarized problems is obtained. Then, we establish the upper and lower semicontinuity of solution mappings for scalarized problem. Finally, the connectedness and path-connectedness of solution sets for symmetric Ky Fan inequality problems are obtained. Our results are new and extend the corresponding ones in the studies.

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Acknowledgements

This first author was supported by the National Natural Science Foundation of China (11301571), the Basic and Advanced Research Project of Chongqing (cstc2018jcyjAX0337), the Program for University Innovation Team of Chongqing (CXTDX201601022), the Education Committee Project Foundation of Bayu Scholar, the Innovation Project for Returned Overseas Scholars in Chongqing (cx2019148) and the open project funded by the Chongqing Key Lab on ORSE (CSSXKFKTZ201801). The second author was supported by the Natural Sciences and Engineering Research Council of Canada. The third author was supported by the National Natural Science Foundation of China (11431004, 11971084). The authors are very grateful to Prof. Lionel Thibault and the anonymous referees for valuable comments and suggestions, which helped to improve the paper.

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Authors and Affiliations

  1. Chongqing JiaoTong University, Chongqing, People’s Republic of China

    Zaiyun Peng

  2. University of British Columbia, Kelowna, Canada

    Ziyuan Wang

  3. Chongqing Normal University, Chongqing, People’s Republic of China

    Xinmin Yang

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  1. Zaiyun Peng
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  2. Ziyuan Wang
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  3. Xinmin Yang
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Correspondence to Zaiyun Peng.

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Communicated by Lionel Thibault.

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Peng, Z., Wang, Z. & Yang, X. Connectedness of Solution Sets for Weak Generalized Symmetric Ky Fan Inequality Problems via Addition-Invariant Sets. J Optim Theory Appl 185, 188–206 (2020). https://doi.org/10.1007/s10957-020-01633-w

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  • DOI: https://doi.org/10.1007/s10957-020-01633-w

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