A new approach about equilibrium problems via Busemann functions. (English) Zbl 1542.90255
Summary: In this paper, we consider the resolvent via Busemann functions introduced by G. de C. Bento et al. [J. Optim. Theory Appl. 195, No. 3, 1087–1105 (2022; Zbl 1542.90254)], and we present a proximal point method for equilibrium problems on Hadamard manifolds. The resolvent in consideration is a natural extension of its counterpart in linear settings, proposed and analyzed by P. L. Combettes and S. A. Hirstoaga [J. Nonlinear Convex Anal. 6, No. 1, 117–136 (2005; Zbl 1109.90079)]. 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.
MSC:
| 90C48 | Programming in abstract spaces |
References:
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