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- W3088998049 abstract "A classical approach to solving two-block separable convex optimization could be the symmetric alternating direction method of multipliers (S-ADMM). However, its convergence may not be guaranteed for a general multi-block case without additional assumptions. Bai et al. proposed a variant of S-ADMM entitled the generalized symmetric ADMM (GS-ADMM), in which the variables are regrouped into two groups firstly. The two groups of variables are updated in a Gauss-Seidel scheme, while the variables within each group are updated in a Jacobi scheme and the Lagrangian multipliers are updated two times. In order to derive its convergence property, the authors add a special proximal term to each subproblem. In this paper, inspired by the partial PPA block-wise ADMM (PPBADMM) [32] proposed by Shen et al., we propose a partially proximal S-ADMM (PPSADMM). In PPSADMM, the special proximal term is only added to the subproblems in the first group as PPBADMM. We perform an extension step on all variables with a fixed step size at the end of each iteration. Without stringent assumptions, we establish the global convergence result and the O(1/t) convergence rate in the ergodic sense for PPSADMM. Its numerical performance is justified on two types of problems." @default.
- W3088998049 created "2020-10-01" @default.
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- W3088998049 date "2021-02-01" @default.
- W3088998049 modified "2023-10-12" @default.
- W3088998049 title "A partially proximal S-ADMM for separable convex optimization with linear constraints" @default.
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- W3088998049 doi "https://doi.org/10.1016/j.apnum.2020.09.016" @default.
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