# Multi-Step Stochastic ADMM in High Dimensions: Applications to Sparse Optimization and Noisy Matrix Decomposition

For sparse optimization, we establish that the modified ADMM method has an optimal convergence rate of $\mathcal{O}(s\log d/T)$, where $s$ is the sparsity level, $d$ is the data dimension and $T$ is the number of steps.

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