Cut-Pursuit Algorithm for Regularizing Nonsmooth Functionals with Graph Total Variation

We present an extension of the cut-pursuit algorithm, introduced by Landrieu and Obozinski (2017), to the graph total-variation regularization of functions with a separable nondifferentiable part. We propose a modified algorithmic scheme as well as adapted proofs of convergence. We also present a heuristic approach for handling the cases in which the values associated to … Read more

A Note on the Forward-Douglas–Rachford Splitting for Monotone Inclusion and Convex Optimization

We shed light on the structure of the “three-operator” version of the forward-Douglas–Rachford splitting algorithm for finding a zero of a sum of maximally monotone operators $A + B + C$, where $B$ is cocoercive, involving only the computation of $B$ and of the resolvent of $A$ and of $C$, separately. We show that it … Read more

Preconditioning of a Generalized Forward-Backward Splitting and Application to Optimization on Graphs

We present a preconditioning of a generalized forward-backward splitting algorithm for finding a zero of a sum of maximally monotone operators \sum_{i=1}^n A_i + B with B cocoercive, involving only the computation of B and of the resolvent of each A_i separately. This allows in particular to minimize functionals of the form \sum_{i=1}^n g_i + … Read more

Generalized Forward-Backward Splitting

This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form $F + \sum_{i=1}^n G_i$, where $F$ has a Lipschitz-continuous gradient and the $G_i$’s are simple in the sense that their Moreau proximity operators are easy to compute. While the forward-backward algorithm cannot deal with more than $n = 1$ non-smooth … Read more