A New Approach About Equilibrium Problems via Busemann Functions

Glaydston C. Bento (), João X. Cruz Neto (), Jurandir O. Lopes (), Ítalo D. L. Melo () and Pedro Silva Filho ()
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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

Journal of Optimization Theory and Applications, 2024, vol. 200, issue 1, No 16, 428-436

Abstract: 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.

Keywords: Equilibrium problem; Proximal method; Busemann function; 47N10; 47H05; 52A37 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02356-4

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