Equilibrium Problems and Proximal Algorithms in Hadamard Spaces
Optimization and Control
2018-07-31 v1 Functional Analysis
Abstract
In this paper, we consider the equilibrium problems and also their regularized problems under the setting of Hadamard spaces. The solution to the regularized problem is represented in terms of resolvent operators. As an essential machinery in the existence of an equilibrium, we first prove that the KKM principle is attained in general Hadamard spaces without assuming the compactness of the closed convex hull of a finite set. We construct the proximal algorithm based on this regularization and give convergence analysis adequately.
Cite
@article{arxiv.1807.10900,
title = {Equilibrium Problems and Proximal Algorithms in Hadamard Spaces},
author = {Poom Kumam and Parin Chaipunya},
journal= {arXiv preprint arXiv:1807.10900},
year = {2018}
}