Convergence study on the logarithmic-quadratic proximal regularization of strictly contractive Peaceman–Rachford splitting method with larger step-size

Abstract

Recently, a strictly contractive Peaceman–Rachford splitting method with logarithmic-quadratic proximal regularization (SPRSM-LQP) was proposed for solving two-block separable convex minimization model. In practical applications, however, the smaller step-size should be strongly avoided. So we actually have the desire of seeking larger step-size whenever possible in order to accelerate the numerical performance. In this paper, we combine Fortin and Glowinski's accelerating techniques with the SPRSM-LQP. Thus a new algorithm with larger step-size is proposed. Under the same assumptions as the SPRSM-LQP, we establish the global convergence of its larger step-size counterpart. Moreover, preliminary numerical results show that the proposed method on a traffic network equilibrium problem is reliable and more efficient with larger step-size.