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.

Keywords:

• Convex programming
• Peaceman–Rachford splitting method
• logarithmic-quadratic proximal regularization
• larger step-size

2010 AMS SUBJECT CLASSIFICATIONS:

• 90C25
• 90C33

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Ke Guo was supported by the Natural Science Foundation of China (grant nos. 11801455, 11571178), Fundamental Research Funds of China West Normal University (grant nos. 17E084, 18B031).