- Generalized Symmetric ADMM for Separable Convex Optimization Jianchao Bai (bjc1987163.com) Jicheng Li (jclimail.xjtu.edu.cn) Fengmin Xu (fengminxumail.xjtu.edu.cn) Hongchao Zhang (hozhangmath.lsu.edu) Abstract: 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 $p \ge 1$ and $q \ge 1$ 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 $\C{O}(1/t)$ 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. Keywords: Separable convex programming, Multiple blocks, Parameter convergence domain, Alternating direction method of multipliers, Global convergence, Complexity, Statistical learning Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Category 2: Global Optimization (Theory ) Citation: Accepted by Comput. Optim. Appl. Download: [PDF]Entry Submitted: 10/31/2016Entry Accepted: 10/31/2016Entry Last Modified: 11/13/2017Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.