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

Author

Listed:
  • Zaiyun Peng

    (Chongqing JiaoTong University)

  • Ziyuan Wang

    (University of British Columbia)

  • Xinmin Yang

    (Chongqing Normal University)

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.

Suggested Citation

  • Zaiyun Peng & Ziyuan Wang & Xinmin Yang, 2020. "Connectedness of Solution Sets for Weak Generalized Symmetric Ky Fan Inequality Problems via Addition-Invariant Sets," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 188-206, April.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:1:d:10.1007_s10957-020-01633-w
    DOI: 10.1007/s10957-020-01633-w
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    References listed on IDEAS

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    Cited by:

    1. Qiuying Li & Sanhua Wang, 2021. "Arcwise Connectedness of the Solution Sets for Generalized Vector Equilibrium Problems," Mathematics, MDPI, vol. 9(20), pages 1-9, October.

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