# Generalized Symmetric ADMM for Separable Convex Optimization

arXiv: https://arxiv.org/abs/1812.03769 · HTML: https://mlsanity.com/paper/1812.03769/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2018.

## Built on by (most cited first, 3 of 3)

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## Abstract (arXiv)

The Alternating Direction Method of Multipliers (ADMM) has been proved to be effective for solving separable convex optimization subject to linear constraints. In this paper, we propose a Generalized Symmetric ADMM (GS-ADMM), which updates the Lagrange multiplier twice with suitable stepsizes, to solve the multi-block separable convex programming. This GS-ADMM 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 ≥ 1 and q ≥ 1 are two integers. The two grouped variables are updated in a it Gauss-Seidel scheme, while the variables within each group are updated in a it Jacobi scheme, which would make it very attractive for a big data setting. By adding proper proximal terms to the subproblems, we specify the domain of the stepsizes to guarantee that GS-ADMM is globally convergent with a worst-case O(1/t) ergodic convergence rate. It turns out that our convergence domain of the stepsizes is significantly larger than other convergence domains in the literature. Hence, the GS-ADMM is more flexible and attractive on choosing and using larger stepsizes of the dual variable. Besides, two special cases of GS-ADMM, which allows using zero penalty terms, are also discussed and analyzed. Compared with several state-of-the-art methods, preliminary numerical experiments on solving a sparse matrix minimization problem in the statistical learning show that our proposed method is effective and promising.