TY - JOUR
T1 - A Unified Algorithmic Framework of Symmetric Gauss-Seidel Decomposition Based Proximal ADMMs for Convex Composite Programming
AU - Chen , Liang
AU - Sun , Defeng
AU - Toh , Kim-Chuan
AU - Zhang , Ning
JO - Journal of Computational Mathematics
VL - 6
SP - 739
EP - 757
PY - 2019
DA - 2019/11
SN - 37
DO - http://doi.org/10.4208/jcm.1803-m2018-0278
UR - https://global-sci.org/intro/article_detail/jcm/13372.html
KW - Convex optimization, Multi-block, Alternating direction method of multipliers, Symmetric Gauss-Seidel decomposition, Majorization.
AB - <p style="text-align: justify;">This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The proposed method unifies
and refines many constructive techniques that were separately developed for the computational efficiency of multi-block ADMM-type algorithms. Specifically, the majorized
augmented Lagrangian functions, the indefinite proximal terms, the inexact symmetric
Gauss-Seidel decomposition theorem, the tolerance criteria of approximately solving the
subproblems, and the large dual step-lengths, are all incorporated in one algorithmic framework, which we named as sGS-imiPADMM. From the popularity of convergent variants
of multi-block ADMMs in recent years, especially for high-dimensional multi-block convex
composite conic programming problems, the unification presented in this paper, as well
as the corresponding convergence results, may have the great potential of facilitating the
implementation of many multi-block ADMMs in various problem settings.</p>