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Cone-Compactness of a Set and Applications to Set-Equilibrium Problems

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  • Marius Durea

    (“Alexandru Ioan Cuza” University
    Iaşi Branch of Romanian Academy)

  • Elena-Andreea Florea

    (“Alexandru Ioan Cuza” University
    Iaşi Branch of Romanian Academy)

Abstract

We study the possibility to get a sequential characterization of the compactness of a set with respect to a cone. Then, we consider some set-equilibrium problems (whose formulations are inspired by set-optimization problems) and in the study of the existence of a solution of these problems we employ the generalized compactness investigated before. Several technical tools are needed throughout the presentation in order to fulfill these objectives. Furthermore, several illustrating examples are presented in order to clearly motivate our theoretical results.

Suggested Citation

  • Marius Durea & Elena-Andreea Florea, 2024. "Cone-Compactness of a Set and Applications to Set-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 200(3), pages 1286-1308, March.
    • Handle: RePEc:spr:joptap:v:200:y:2024:i:3:d:10.1007_s10957-024-02384-8
    DOI: 10.1007/s10957-024-02384-8
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    References listed on IDEAS

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    1. B. Jiménez & V. Novo & A. Vílchez, 2020. "Characterization of set relations through extensions of the oriented distance," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 89-115, February.
    2. Marius Durea & Radu Strugariu, 2017. "Vectorial penalization for generalized functional constrained problems," Journal of Global Optimization, Springer, vol. 68(4), pages 899-923, August.
    3. M. Durea & R. Strugariu, 2011. "Existence conditions for generalized vector variational inequalities," Annals of Operations Research, Springer, vol. 191(1), pages 255-262, November.
    4. L. Huerga & B. Jiménez & V. Novo, 2022. "New Notions of Proper Efficiency in Set Optimization with the Set Criterion," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 878-902, December.
    5. Jun-Yi Fu, 2005. "Vector Equilibrium Problems. Existence Theorems and Convexity of Solution Set," Journal of Global Optimization, Springer, vol. 31(1), pages 109-119, January.
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