Name
Abstract | ||
|---|---|---|
The alternating direction method of multipliers (ADMM) has been widely used for solving structured convex optimization problems. In particular, the ADMM can solve convex programs that minimize the sum of N convex functions whose variables are linked by some linear constraints. While the convergence of the ADMM for N = 2 was well established in the literature, it remained an open problem for a long time whether the ADMM for N >= 3 is still convergent. Recently, it was shown in [Chen et al., Math. Program. (2014), DOI 10.1007/s10107-014-0826-5.] that without additional conditions the ADMM for N >= 3 generally fails to converge. In this paper, we show that under some easily verifiable and reasonable conditions the global linear convergence of the ADMM when N >= 3 can still be ensured, which is important since the ADMM is a popular method for solving large-scale multiblock optimization models and is known to perform very well in practice even when N >= 3. Our study aims to offer an explanation for this phenomenon. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1137/140971178 | SIAM JOURNAL ON OPTIMIZATION |
Keywords | Field | DocType |
alternating direction method of multipliers,global linear convergence,convex optimization | Convergence (routing),Mathematical optimization,Chen,Open problem,Regular polygon,Verifiable secret sharing,Convex function,Rate of convergence,Convex optimization,Mathematics | Journal |
Volume | Issue | ISSN |
25 | 3 | 1052-6234 |
Citations | PageRank | References |
39 | 1.07 | 18 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tianyi Lin | 1 | 147 | 11.79 |
| Shiqian Ma | 2 | 1068 | 63.48 |
| Shuzhong Zhang | 3 | 2808 | 181.66 |