2018/01/09 by Chong Li, Li, Chong, Xiangmei Wang +5
Computer Science · Mathematics · #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1801.02752
openalex publication_date 2018/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.