On the ergodic convergence rates of a first-order primal-dual algorithm.

Antonin Chambolle (1) , Thomas Pock (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 ICG - Institute for Computer Graphics and Vision [Graz]

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.

Mots clés: Saddle-point problems; first order algorithms; primal-dual algorithms; convergence rates; ergodic convergence; Bregman distances

Domaines: Analyse numérique [math.NA]; Optimisation et contrôle [math.OC]

Antonin Chambolle, Thomas Pock. On the ergodic convergence rates of a first-order primal-dual algorithm.. Mathematical Programming, Series A, 2016, 159 (1-2), pp.253-287. ⟨hal-01151629v2⟩