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Overall Objectives
Application Domains
New Results
Bilateral Contracts and Grants with Industry
Bibliography
Overall Objectives
Application Domains
New Results
Bilateral Contracts and Grants with Industry
Bibliography


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 [41] , we present a preconditioning of a generalized forward-backward splitting algorithm for finding a zero of a sum of maximally monotone operators i=1nAi+B with B cocoercive, involving only the computation of B and of the resolvent of each Ai separately. This allows in particular to minimize functionals of the form i=1ngi+f with f smooth, using only the gradient of f and the proximity operator of each gi 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 Ai for some i. 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.