期刊
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
卷 66, 期 2, 页码 327-343出版社
SPRINGER
DOI: 10.1007/s10589-016-9864-7
关键词
Alternating direction method of multipliers (ADMM); Convergence; Counterexample; Large step-length
资金
- China Scholarship Council
- National Natural Science Foundation of China [11271117]
- Ministry of Education, Singapore, Academic Research Fund [R-146-000-194-112]
This note serves two purposes. Firstly, we construct a counterexample to show that the statement on the convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex optimization problems in a highly influential paper by Boyd et al. (Found Trends Mach Learn 3(1):1-122, 2011) can be false if no prior condition on the existence of solutions to all the subproblems involved is assumed to hold. Secondly, we present fairly mild conditions to guarantee the existence of solutions to all the subproblems of the ADMM and provide a rigorous convergence analysis on the ADMM with a computationally more attractive large step-length that can even exceed the practically much preferred golden ratio of .
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