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Weighted iteration complexity of the sPADMM on the KKT residuals for convex composite optimization

In this paper we establish an $\mathcal{O}({1}/{k})$ weighted iteration complexity on the KKT residuals yielded by the sPADMM (semi-proximal alternating direction method of multiplier) for the convex composite optimization problem. This result, which is derived with the help of a novel generalized HPE (hybrid proximal extra-gradient) iteration formula, first fills the gap on the ergodic iteration complexity of the classic ADMM with a large step-size and its many proximal variants.

preprint2016arXivOpen access
Li ShenShaohua Pan
math.OC
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Li ShenShaohua Pan

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