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Stability of Optimal Points with Respect to Improvement Sets

Author

Listed:
  • Yu Han

    (Jiangxi University of Finance and Economics)

  • Ke Quan Zhao

    (Chongqing Normal University)

Abstract

The aim of this paper is to study the stability of optimal point sets based on the improvement set E by using the scalarization method and the density results. Under the convergence of a sequence of sets in the sense of Wijsman, we derive the convergence of the sets of E-optimal points, weak E-optimal points, E-quasi-optimal points, E-Benson proper optimal points, E-super optimal points and E-strictly optimal points in the sense of Wijsman. Moreover, we obtain the semicontinuity of E-optimal point mapping, weak E-optimal point mapping, E-quasi-optimal point mapping, E-Benson proper optimal point mapping, E-super optimal point mapping and E-strictly optimal point mapping. Finally, we make a new attempt to establish Lipschitz continuity of these E-optimal point mappings under some suitable conditions.

Suggested Citation

  • Yu Han & Ke Quan Zhao, 2023. "Stability of Optimal Points with Respect to Improvement Sets," Journal of Optimization Theory and Applications, Springer, vol. 199(3), pages 904-930, December.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:3:d:10.1007_s10957-023-02308-y
    DOI: 10.1007/s10957-023-02308-y
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