Equilibrium Problems and Proximal Algorithms in Hadamard Spaces

Authors

  • P. Kumam KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTARG) Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand http://orcid.org/0000-0002-5463-4581
  • P. Chaipunya KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTARG) Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand

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 a piece of 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.

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Published

2017-12-31

How to Cite

Kumam, P., & Chaipunya, P. (2017). Equilibrium Problems and Proximal Algorithms in Hadamard Spaces. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 8(2), 155-172. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/565

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Section

Research Article

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