The symmetric alternating direction method of multipliers (S-ADMM) is a classical effective method for solving two-block separable convex optimization. However, its convergence may not be guaranteed for multi-block case providing there is no additional assumptions. In this paper, we propose a partial PPa S-ADMM (referred as P3SADMM), which updates the Lagrange multiplier twice with suitable stepsizes and adds a special proximal term to the first subproblem, to solve the multi-block separable convex optimization. The P3SADMM partitions the data into two group variables so that one group consists of $p$ block variables while the other has $q$ block variables, where $p\geq 1$ and $q\geq1$ are two integers. In addition, we add a special proximal terms to the subproblems in the first group, i.e., the residual subproblems are intact. At the end of each iteration, an extension step on all variables is performed with a fixed step size. Without any additional assumptions, we prove the global convergence of the P3SADMM. Finally, some numerical results show that our proposed method is effective and promising.
Tech Report 01, NUFE, 03/20