Section: New Results
Preconditioning of a Generalized Forward-Backward Splitting and Application to Optimization on Graphs
Participant : Loïc Landrieu [correspondent] .
Collaboration with Hugo Raguet.
In  , we present a preconditioning of a generalized forward-backward splitting algorithm for finding a zero of a sum of maximally monotone operators with cocoercive, involving only the computation of and of the resolvent of each separately. This allows in particular to minimize functionals of the form with smooth, using only the gradient of and the proximity operator of each separately. By adapting the underlying metric, such preconditioning can serve two practical purposes: first, it might accelerate the convergence, or second, it might simplify the computation of the resolvent of for some . In addition, in many cases of interest, our preconditioning strategy allows the economy of storage and computation concerning some auxiliary variables. In particular, we show how this approach can handle large-scale, non-smooth, convex optimization problems structured on graphs, which arises in many image processing or learning applications, and that it compares favourably to alternatives in the literature.