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Mathematics > Optimization and Control

arXiv:2207.04015 (math)
[Submitted on 8 Jul 2022 (v1), last revised 21 Apr 2024 (this version, v3)]

Title:Convergence Analyses of Davis-Yin Splitting via Scaled Relative Graphs

Authors:Jongmin Lee, Soheun Yi, Ernest K. Ryu
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Abstract:Davis-Yin splitting (DYS) has found a wide range of applications in optimization, but its linear rates of convergence have not been studied extensively. The scaled relative graph (SRG) simplifies the convergence analysis of operator splitting methods by mapping the action of the operator onto the complex plane, but the prior SRG theory did not fully apply to the DYS operator. In this work, we formalize an SRG theory for the DYS operator and use it to obtain tighter contraction factors.
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:2207.04015 [math.OC]
  (or arXiv:2207.04015v3 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2207.04015

Submission history

From: Jongmin Lee [view email]
[v1] Fri, 8 Jul 2022 17:08:11 UTC (453 KB)
[v2] Thu, 18 Aug 2022 12:45:22 UTC (493 KB)
[v3] Sun, 21 Apr 2024 08:43:36 UTC (648 KB)
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