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A New Approach About Equilibrium Problems via Busemann Functions

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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.

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Acknowledgements

The authors was supported in part by CNPq grants 314106/2020-0 and 302156/2022-4.

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Authors and Affiliations

  1. Universidade Federal de Goiás, Goias, Brazil

    Glaydston de C. Bento

  2. Universidade Federal do Piauí, Teresina, Piauí, Brazil

    João X. Cruz Neto, Jurandir O. Lopes, Ítalo D. L. Melo & Pedro Silva Filho

Authors
  1. Glaydston de C. Bento
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  2. João X. Cruz Neto
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  3. Jurandir O. Lopes
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  4. Ítalo D. L. Melo
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  5. Pedro Silva Filho
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Correspondence to Glaydston de C. Bento.

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Communicated by Sándor Zoltán Németh.

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de C. Bento, G., Neto, J.X.C., Lopes, J.O. et al. A New Approach About Equilibrium Problems via Busemann Functions. J Optim Theory Appl 200, 428–436 (2024). https://doi.org/10.1007/s10957-023-02356-4

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  • DOI: https://doi.org/10.1007/s10957-023-02356-4

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