# Operator Splitting Performance Estimation: Tight contraction factors and optimal parameter selection

arXiv: https://arxiv.org/abs/1812.00146 · HTML: https://mlsanity.com/paper/1812.00146/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2018.

## Built on by (most cited first, 13 of 13)

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## Abstract (arXiv)

We propose a methodology for studying the performance of common splitting methods through semidefinite programming. We prove tightness of the methodology and demonstrate its value by presenting two applications of it. First, we use the methodology as a tool for computer-assisted proofs to prove tight analytical contraction factors for Douglas--Rachford splitting that are likely too complicated for a human to find bare-handed. Second, we use the methodology as an algorithmic tool to computationally select the optimal splitting method parameters by solving a series of semidefinite programs.