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Improved pointwise iteration-complexity of a regularized ADMM

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Improved pointwise iteration-complexity of a regularized ADMM
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30
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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In this talk, we present a regularized variant of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex programs. The pointwise iteration-complexity of the new variant is better than the corresponding one for the standard ADMM method and, up to a logarithmic term, is identical to the ergodic iteration-complexity of the latter method. We discuss how this regularized ADMM can be seen as an instance of a regularized hybrid proximal extragradient framework whose error condition at each iteration includes both a relative error and a summable error.