A modification of the forward-backward splitting method for maximal monotone mappings

In this paper, we propose a modification of the forward-backward splitting method for maximal monotone mappings, where we adopt a new step-size scheme in generating the next iterate. This modification is motivated by the ingenious rule proposed by He and Liao in modified Korpelevich's extra-gradient method [13]. Under suitable conditions, we prove the global convergence of the new algorithm. We apply our method to solve some monotone variational inequalities and report its numerical results. Comparisons with modified Khobotov-Korpelevich's extragradient method [13,14] and Tseng's method [30] show the significance of our work.