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The convergence rate of the proximal alternating direction method of multipliers with indefinite proximal regularization.
- Source :
- Journal of Inequalities & Applications; 1/14/2017, Vol. 2017 Issue 1, p1-15, 15p
- Publication Year :
- 2017
-
Abstract
- The proximal alternating direction method of multipliers (P-ADMM) is an efficient first-order method for solving the separable convex minimization problems. Recently, He et al. have further studied the P-ADMM and relaxed the proximal regularization matrix of its second subproblem to be indefinite. This is especially significant in practical applications since the indefinite proximal matrix can result in a larger step size for the corresponding subproblem and thus can often accelerate the overall convergence speed of the P-ADMM. In this paper, without the assumptions that the feasible set of the studied problem is bounded or the objective function's component $\theta_{i}(\cdot)$ of the studied problem is strongly convex, we prove the worst-case $\mathcal{O}(1/t)$ convergence rate in an ergodic sense of the P-ADMM with a general Glowinski relaxation factor $\gamma\in(0,\frac{1+\sqrt{5}}{2})$ , which is a supplement of the previously known results in this area. Furthermore, some numerical results on compressive sensing are reported to illustrate the effectiveness of the P-ADMM with indefinite proximal regularization. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10255834
- Volume :
- 2017
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of Inequalities & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 120738075
- Full Text :
- https://doi.org/10.1186/s13660-017-1295-1