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A New Approach About Equilibrium Problems via Busemann Functions

Author

Listed:
  • Glaydston C. Bento

    (Universidade Federal de Goiás)

  • João X. Cruz Neto

    (Universidade Federal do Piauí)

  • Jurandir O. Lopes

    (Universidade Federal do Piauí)

  • Ítalo D. L. Melo

    (Universidade Federal do Piauí)

  • Pedro Silva Filho

    (Universidade Federal do Piauí)

Abstract

In this paper, we consider the resolvent via Busemann functions introduced by Bento, Cruz Neto, Melo (J Optim Theory Appl 195:1087–1105, 2022), and we present a proximal point method for equilibrium problems on Hadamard manifold. The resolvent in consideration is a natural extension of its counterpart in linear settings, proposed and analyzed by Combettes and Hirstoaga (J Nonlinear Convex Anal 6:117–136, 2005). The advantage of using this resolvent is that the term performing regularization is a convex function in general Hadamard manifolds, allowing us to explore the asymptotic behavior of the proximal point method to solve equilibrium problems.

Suggested Citation

  • Glaydston C. Bento & João X. Cruz Neto & Jurandir O. Lopes & Ítalo D. L. Melo & Pedro Silva Filho, 2024. "A New Approach About Equilibrium Problems via Busemann Functions," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 428-436, January.
    • Handle: RePEc:spr:joptap:v:200:y:2024:i:1:d:10.1007_s10957-023-02356-4
    DOI: 10.1007/s10957-023-02356-4
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    References listed on IDEAS

    as
    1. E. E. A. Batista & G. C. Bento & O. P. Ferreira, 2015. "An Existence Result for the Generalized Vector Equilibrium Problem on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 550-557, November.
    2. G. C. Bento & J. X. Cruz Neto & P. A. Soares & A. Soubeyran, 2022. "A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires," Annals of Operations Research, Springer, vol. 316(2), pages 1301-1318, September.
    Full references (including those not matched with items on IDEAS)

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