A generic first-order primal-dual method for convex optimization involving Lipschitzian, proximable and linear composite terms

Laurent Condat (1)

1 GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen

We propose a new first-order algorithm for solving jointly the primal and dual formulations of large-scale convex minimization problems involving the sum of a smooth function with Lipschitzian gradient, nonsmooth proximable functions and linear composite functions. The gradient and the linear operators present in the formulation are called explicitly, while the other functions are processed individually via their proximity operators. This work brings together and notably extends several classical splitting schemes like the forward-backward and Douglas-Rachford methods, as well as recent primal-dual methods designed for linear composite terms.

Mots clés: convex and nonsmooth optimization; splitting methods; primal-dual; forward-backward; Douglas-Rachford; monotone inclusions

Domaines: Optimisation et contrôle [math.OC]

Laurent Condat. A generic first-order primal-dual method for convex optimization involving Lipschitzian, proximable and linear composite terms. 2011. ⟨hal-00609728v2⟩