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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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    References listed on IDEAS

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    1. Akhtar A. Khan & Dumitru Motreanu, 2015. "Existence Theorems for Elliptic and Evolutionary Variational and Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 1136-1161, December.
    2. Yu Han & Nan-jing Huang, 2018. "Existence and Connectedness of Solutions for Generalized Vector Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 65-85, October.
    3. Nishimura, Kazuo & Friedman, James, 1981. "Existence of Nash Equilibrium in n Person Games without Quasi-Concavity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(3), pages 637-648, October.
    4. Didier Aussel & Parin Chaipunya, 2024. "Variational and Quasi-Variational Inequalities Under Local Reproducibility: Solution Concept and Applications," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1531-1563, November.
    5. John Cotrina & Javier Zúñiga, 2019. "Quasi-equilibrium problems with non-self constraint map," Journal of Global Optimization, Springer, vol. 75(1), pages 177-197, September.
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