Degenerate Preconditioned Proximal Point Algorithms

In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak results under mild assumptions that can be easily employed in context splitting methods for monotone inclusion and convex minimization problems. Moreover, show degeneracy preconditioner allows reduction variables involved iteration updates. strength proposed framework algorithms, providing new simplified proofs highlighting link between existing schemes, such as Chambolle-Pock, Forward Douglas-Rachford Peaceman-Rachford, study from perspective. The devise flexible schemes provides ways generalize case sum many terms. As an example, present sequential generalization along with numerical experiments demonstrate its interest nonsmooth optimization.