## Abdellah Bnouhachem, Michael Th. Rassias, A Bregman proximal Peaceman-Rachford splitting method for convex programming

Full Text: PDF
DOI: 10.23952/asvao.4.2022.2.01
Volume 4, Issue 2, 1 August 2022, Pages 129-143

Abstract. In this paper, based on the Bregman distance and the proximal Peaceman-Rachford splitting method (PRSM), we propose a Bregman proximal Peaceman-Rachford splitting method for solving a separable convex minimization model. We establish the relationship between two parameters under which we prove the global convergence of the algorithm. The $O(1/t)$ convergence rate of the proposed method in the ergodic sense is also studied. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method.