Extending the ergodic convergence rate of the proximal ADMM
نویسندگان
چکیده
Pointwise and ergodic iteration-complexity results for the proximal alternating direction method of multipliers (ADMM) for any stepsize in (0, (1 + √ 5)/2) have been recently established in the literature. In addition to giving alternative proofs of these results, this paper also extends the ergodic iteration-complexity result to include the case in which the stepsize is equal to (1+ √ 5)/2. As far as we know, this is the first ergodic iteration-complexity for the stepsize (1 + √ 5)/2 obtained in the ADMM literature. These results are obtained by showing that the proximal ADMM is an instance of a non-Euclidean hybrid proximal extragradient framework whose pointwise and ergodic convergence rate are also studied. 2000 Mathematics Subject Classification: 47H05, 47J22, 49M27, 90C25, 90C30, 90C60, 65K10.
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