Convergence of One-Step Projection Methods for Equilibrium Problems Given by a Sum of Two Bifunctions

The paper introduces a one-step projection method for solving a pseudomonotone equilibrium problem given by a sum of two bifunctions in Hilbert spaces. Compared with the existing splitting methods, our algorithm is simpler as it only requires one projection onto the feasible set at each iteration. Under standard assumptions, the weak convergence of the new algorithm is established. Besides, we present a strong convergence result of a regularized version of the proposed method. Finally, we perform two numerical examples to demonstrate the promise of the proposed algorithms.