Convergence analysis of positive-indefinite proximal ADMM with a Glowinski's relaxation factor

In this paper, we propose a modified positive-indefinite proximal linearized ADMM (PIPL-ADMM) with a larger Glowinski's relaxation factor for solving two-block linearly constrained separable convex programming by variational inequality technique. We investigate the internal relationships between the step size coefficient and the penalty coefficient to identify the convergence of PIPL-ADMM. The convergence of PIPL-ADMM and its convergence rate measured by the iteration complexity are established in the ergodic case. Numerical experiments are reported to illustrate the efficiency of the proposed methods.