title: The convergence rate of the proximal alternating direction method of multipliers with indefinite proximal regularization.
abstract: The proximal alternating direction method of multipliers (P-ADMM) is an efficient first-order method for solving the separable convex minimization problems. Recently, Heet al.have further studied the P-ADMM and relaxed the proximal regularization matrix of its second subproblem to be indefinite. This is especially significant in practical applications since the indefinite proximal matrix can result in a larger step size for the corresponding subproblem and thus can often accelerate the overall convergence speed of the P-ADMM. In this paper, without the assumptions that the feasible set of the studied problem is bounded or the objective function's component [Formula: see text] of the studied problem is strongly convex, we prove the worst-case [Formula: see text] convergence rate in an ergodic sense of the P-ADMM with a general Glowinski relaxation factor [Formula: see text], which is a supplement of the previously known results in this area. Furthermore, some numerical results on compressive sensing are reported to illustrate the effectiveness of the P-ADMM with indefinite proximal regularization.
authors.affiliation: School of Management, Qufu Normal University, Shandong, 276826 P.R. China ; School of Mathematics and Statistics, Zaozhuang University, Shandong, 277160 P.R. China.
authors.forename: Min
authors.initials: M
authors.lastname: Sun
authors.affiliation: School of Data Sciences, Zhejiang University of Finance and Economics, Hangzhou, 310018 China.
authors.forename: Jing
authors.initials: J
authors.lastname: Liu
keywords: compressive sensing; proximal alternating direction method of multipliers; two-block separable convex minimization problem