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Equilibrium problems on Riemannian manifolds with applications

 

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Opened Access Equilibrium problems on Riemannian manifolds with applications
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Author: Wang, Xiangmei
López Acedo, Genaro
Li, Chong
Yao, Jen-Chih
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2019-05-15
Published in: Journal of Mathematical Analysis and Applications, 473 (2), 866-891.
Document type: Article
Abstract: We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable variational inequality problem on Riemannian manifolds, and is completely different from previous ones on this topic in the literature. As applications, the corresponding results for the mixed variational inequality and the Nash equilibrium are obtained. Moreover, we formulate and analyze the convergence of the proximal point algorithm for the equilibrium problem. In particular, correct proofs are provided for the results claimed in J. Math. Anal. Appl. 388, 61-77, 2012 (i.e., Theorems 3.5 and 4.9 there) regarding the existence of the mixed variational inequality and the domain of the resolvent for the equilibrium problem on Hadamard manifolds.
Size: 376.7Kb
Format: PDF

URI: https://hdl.handle.net/11441/83899

DOI: 10.1016/j.jmaa.2018.12.073

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