@Article{CSIAM-AM-3-448,
author = {Bai , JianchaoHan , DerenSun , Hao and Zhang , Hongchao},
title = {Convergence on a Symmetric Accelerated Stochastic ADMM with Larger Stepsizes},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2022},
volume = {3},
number = {3},
pages = {448--479},
abstract = {<p style="text-align: justify;">In this paper, we develop a symmetric accelerated stochastic Alternating
Direction Method of Multipliers (SAS-ADMM) for solving separable convex optimization problems with linear constraints. The objective function is the sum of a possibly
nonsmooth convex function and an average function of many smooth convex functions. Our proposed algorithm combines both ideas of ADMM and the techniques of
accelerated stochastic gradient methods possibly with variance reduction to solve the
smooth subproblem. One main feature of SAS-ADMM is that its dual variable is symmetrically updated after each update of the separated primal variable, which would allow a more flexible and larger convergence region of the dual variable compared with
that of standard deterministic or stochastic ADMM. This new stochastic optimization
algorithm is shown to have ergodic converge in expectation with $\mathcal{O}(1/T)$ convergence
rate, where $T$ denotes the number of outer iterations. Our preliminary experiments
indicate the proposed algorithm is very effective for solving separable optimization
problems from big-data applications. Finally, 3-block extensions of the algorithm and
its variant of an accelerated stochastic augmented Lagrangian method are discussed in
the appendix.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2021-0021},
url = {http://global-sci.org/intro/article_detail/csiam-am/20969.html}
}