We consider the linearly constrained separable convex optimization problem whose objective function is separable w.r.t. $m$ blocks of variables. A bunch of methods have been proposed and well studied. Specifically, a modified strictly contractive Peaceman-Rachford splitting method (SC-PRCM) has been well studied in the literature for the special case of $m=3$. Based on the modified SC-PRCM, we present a modified proximal symmetric ADMM (MPS-ADMM) to solve the multi-block problems. In MPS-ADMM, all subproblems but the first one are attached with a simple proximal term, and the multipliers are updated twice. In addition, at the end of each iteration, the output is corrected via a simple correction step. Without stringent assumptions, we establish the global convergence result for the new algorithms. Preliminary numerical results show that our proposed methods are effective for solving the linearly constrained quadratic programming and the robust principal component analysis problems.
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