An extragradient method for non-monotone equilibrium problems on Hadamard manifolds with applications

In the present paper, we consider a non-monotone equilibrium problem on Hadamard manifolds and define Armijo's type extragradient algorithm for the proposed equilibrium problem. The introduced algorithm does not require objective bifunction's monotonicity and the solution set's nonemptiness. A convergence result of our algorithm under very mild assumptions is presented. Moreover, we investigate the applications of the established results to the non-monotone set-valued variational inequalities and the generalized Nash equilibrium problems from the considered method. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.