A New Non-Euclidean Proximal Method for Equilibrium Problems
The paper analyzes the convergence of a new iterative algorithm for approximating solutions of equilibrium problems in finite-dimensional real vector space. Using the Bregman distance instead of the Euclidean, we modified the recently proposed two-stage proximal algorithm. The Bregman distance allows us to take into account the geometry of an admissible set effectively in some important cases. Namely, with the suitable choice of distance, we obtain a method with explicitly solvable auxiliary problems on the iterative steps. The convergence of the algorithm is proved under the assumption that the solution exists and the bifunction is pseudo-monotone and Lipschitz-type.
KeywordsEquilibrium problem Two-stage proximal method Bregman distance Pseudo-monotonicity Lipschitz property Convergence