On the ergodic convergence rates of a first-order primal-dual algorithm.
Résumé
We revisit the proofs of convergence for a first order primal-dual algorithm for convex optimization which we have studied a few years ago. In particular, we prove rates of convergence for a more general version, with simpler proofs and more complete results. The new results can deal with explicit terms and nonlinear proximity operators in spaces with quite general norms.
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Cite 10.1007/s10107-015-0957-3 Autre Chambolle, A., & Pock, T. (2015). On the ergodic convergence rates of a first-order primal–dual algorithm. Mathematical Programming, 159(1–2), 253–287. https://doi.org/10.1007/s10107-015-0957-3