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Quasi-Optimization Problems: Existence, Iterative Algorithms and Well-Posedness

Author

Listed:
  • Shengda Zeng

    (Chongqing Normal University)

  • Qing Nie

    (Chongqing Jiaotong University)

  • Calogero Vetro

    (Department of Mathematics and Computer Science)

Abstract

The aim of this article is to introduce and study a quasi-optimization problem (QOP, for short) on an infinite dimensional Banach space. First, under mild assumptions, we deliver three existence theorems for (QOP) by employing Kluge’s fixed point principle for multivalued operators. Then, several sufficient and necessary conditions for a solution of (QOP) are proved. Furthermore, two iterative algorithms are proposed and the convergence results are obtained. Finally, the well-posedness and generalized well-posedness of (QOP) are introduced and its equivalent metric characteristic is established.

Suggested Citation

  • Shengda Zeng & Qing Nie & Calogero Vetro, 2025. "Quasi-Optimization Problems: Existence, Iterative Algorithms and Well-Posedness," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-21, August.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:2:d:10.1007_s10957-025-02701-9
    DOI: 10.1007/s10957-025-02701-9
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