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Semicontinuity Property of Approximate Solution Mappings in Bifunction-Set Optimization

Author

Listed:
  • Pham Huu Sach

    (Institute of Mathematics,Vietnam Academy of Science and Technology)

  • Le Anh Tuan

    (Nong Lam University)

Abstract

Lower and upper semicontinuity results for the approximate solution mapping of the parametric bifunction-set optimization problem are established under new assumptions that are quite different from the ones used previously in the case of exact solution mapping. Applications to the stability study of the approximate solution mapping of a parametric Kuroiwa set optimization problem and a parametric vector Ky Fan inequality problem are given. To our knowledge, our stability results are original. Several examples are provided.

Suggested Citation

  • Pham Huu Sach & Le Anh Tuan, 2021. "Semicontinuity Property of Approximate Solution Mappings in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 202-228, October.
    • Handle: RePEc:spr:joptap:v:191:y:2021:i:1:d:10.1007_s10957-021-01931-x
    DOI: 10.1007/s10957-021-01931-x
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    References listed on IDEAS

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    1. César Gutiérrez & Enrico Miglierina & Elena Molho & Vicente Novo, 2016. "Convergence of Solutions of a Set Optimization Problem in the Image Space," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 358-371, August.
    2. X. Li & S. Li, 2011. "Continuity of approximate solution mappings for parametric equilibrium problems," Journal of Global Optimization, Springer, vol. 51(3), pages 541-548, November.
    3. Pham Huu Sach, 2018. "Solution Existence in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 1-16, January.
    4. Pham Huu Sach, 2018. "Stability Property in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 376-398, May.
    Full references (including those not matched with items on IDEAS)

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