Convergence Analyses of Davis-Yin Splitting via Scaled Relative Graphs II: Convex Optimization Problems

TL;DR

This paper extends the analysis of Davis-Yin splitting (DYS) iterations using scaled relative graphs to convex optimization problems, achieving state-of-the-art linear convergence rates.

Contribution

It applies SRG analysis to convex optimization, providing improved convergence rate results for DYS iterations.

Findings

Achieves state-of-the-art linear convergence rates for DYS on convex problems.

Extends SRG analysis framework to convex optimization scenarios.

Provides theoretical convergence guarantees for DYS methods.

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.