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Convergence of solutions to set optimization problems with variable ordering structures

Author

Listed:
  • L. Q. Anh

    (Cantho University)

  • D. V. Hien

    (Ho Chi Minh City University of Industry and Trade)

Abstract

In this article, we consider set optimization problems with variable ordering structures. Within the framework of the set less order relation with variable ordering structures, we investigate the existence, the upper convergence, and the lower convergence of solutions to such problems in the image spaces. For both the existence and the upper convergence of solutions, we employ new techniques to obtain various results without assuming the compactness of the constraint sets. Additionally, we utilize the domination property concerning the variable ordering cones to address the lower convergence of solutions. The obtained results are presented in several versions from different aspects for convenient comparison with existing results. Many examples are provided to illustrate the novelty of our results or to compare them with existing ones in the literature.

Suggested Citation

  • L. Q. Anh & D. V. Hien, 2025. "Convergence of solutions to set optimization problems with variable ordering structures," Journal of Global Optimization, Springer, vol. 91(3), pages 677-699, March.
    • Handle: RePEc:spr:jglopt:v:91:y:2025:i:3:d:10.1007_s10898-024-01452-7
    DOI: 10.1007/s10898-024-01452-7
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    References listed on IDEAS

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    1. Truong Q. Bao & Lidia Huerga & Bienvenido Jiménez & Vicente Novo, 2020. "Necessary Conditions for Nondominated Solutions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 826-842, September.
    2. 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.
    3. Lam Quoc Anh & Tran Quoc Duy & Dinh Vinh Hien & Daishi Kuroiwa & Narin Petrot, 2020. "Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 416-432, May.
    4. Gabriele Eichfelder & Maria Pilecka, 2016. "Set Approach for Set Optimization with Variable Ordering Structures Part I: Set Relations and Relationship to Vector Approach," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 931-946, December.
    5. Gabriele Eichfelder, 2011. "Optimal Elements in Vector Optimization with a Variable Ordering Structure," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 217-240, November.
    6. Gabriele Eichfelder & Maria Pilecka, 2016. "Set Approach for Set Optimization with Variable Ordering Structures Part II: Scalarization Approaches," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 947-963, December.
    7. Michel H. Geoffroy, 2019. "A topological convergence on power sets well-suited for set optimization," Journal of Global Optimization, Springer, vol. 73(3), pages 567-581, March.
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