- A symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming Liu Jing (liujingta126.com) Duan Yongrui (yrduan163.com) Sun Min (ziyouxiaodou163.com) Abstract: \ys{This paper introduces} a symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming \ys{with linear equality constraints, which inherits the superiorities of the classical alternating direction method of multipliers (ADMM), and extends the feasible set of the relaxation factor $\alpha$ of the generalized ADMM to the infinite interval $[1,+\infty)$}. \ys{Under the conditions that the objective function is convex and the solution set is nonempty}, we \ys{establish} the \ys{convergence} results of the proposed method, including the global convergence, the worst-case $\mathcal{O}(1/k)$ convergence rate in both the ergodic and non-ergodic senses, where $k$ denotes the iteration counter. Numerical experiments to decode a sparse signal arising in compressed sensing are included to illustrate the efficiency of the new method. Keywords: Alternating direction method of multipliers; convex programming; mixed variational inequalities; compressed sensing. Category 1: Convex and Nonsmooth Optimization Citation: Download: [PDF]Entry Submitted: 05/01/2017Entry Accepted: 05/01/2017Entry Last Modified: 05/02/2017Modify/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.