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Pointwise and ergodic convergence rates of a variable metric proximal ADMM

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Pointwise and ergodic convergence rates of a variable metric proximal ADMM
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30
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
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In this talk, we discuss pointwise and ergodic convergence rates for a variable metric proximal alternating direction method of multiplicas (VM-PADMM) for solving linearly constrained convex optimization problems. The VM-PADMM can be seen as a class of ADMM variants, allowing the use of degenerate metrics (defined by noninvertible linear operators). We first propose and study nonasymptotic convergence rates of a variable metric hybrid proximal extragradient (VM-HPE) framework for solving monotone inclusions. Then, the convergence rates for the VM-PADMM are obtained essentially by showing that it falls within the latter framework.