SMPM is a stochastic multi-proximal method that recovers several existing algorithms as special cases and provides new linear and accelerated sublinear convergence guarantees for nonsmooth convex problems.
Convergence Analyses of Davis-Yin Splitting via Scaled Relative Graphs II: Convex Optimization Problems
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abstract
The prior work of [SIAM J. Optim., 2025] used scaled relative graphs (SRG) to analyze the convergence of Davis--Yin splitting (DYS) iterations on monotone inclusion problems. In this work, we use this machinery to analyze DYS iterations on convex optimization problems and obtain state-of-the-art linear convergence rates.
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The Stochastic Multi-Proximal Method for Nonsmooth Optimization
SMPM is a stochastic multi-proximal method that recovers several existing algorithms as special cases and provides new linear and accelerated sublinear convergence guarantees for nonsmooth convex problems.