  


Preconditioning of a Generalized ForwardBackward Splitting and Application to Optimization on Graphs
Hugo Raguet (hugo.raguetgmail.com) Abstract: We present a preconditioning of a generalized forwardbackward 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 + f with f smooth. 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 A_i 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 largescale, nonsmooth, convex optimization problems structured on graphs, which arises in many image processing or learning applications, and that it compares favorably to alternatives in the literature. Keywords: preconditioning; forwardbackward splitting; monotone operator splitting; proximal splitting; nonsmooth convex optimization; quasiNewton methods; graph learning; graph sparsity; total variation; MumfordShah functional; geoinformatics Category 1: Convex and Nonsmooth Optimization Category 2: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity ) Citation: Download: [PDF] Entry Submitted: 04/21/2015 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  