摘要
This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alt ernating direction met hods 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 algor计hms.Specifically,the majorized augmented Lagrangian functions,the indefinite proximal terms,the inexact symmetrie Gauss-Seidel decomposition theorem,the tolerance criteria of approximately solving the subproblems,and the large dual step-lengths,are all incorporated in one algoi?计hmic 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 presen ted in this paper,as well as the corresponding convergence results,may have the great potential of facilitating the implemen tation of many multi-block ADMMs in various problem set tings.
