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A symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming

Liu Jing (liujingta***at***126.com)
Duan Yongrui (yrduan***at***163.com)
Sun Min (ziyouxiaodou***at***163.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:

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Entry Submitted: 05/01/2017
Entry Accepted: 05/01/2017
Entry Last Modified: 05/02/2017

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