SIAM Journal on Numerical Analysis· 2012Q1
On the $O(1/n)$ Convergence Rate of the Douglas–Rachford Alternating Direction Method
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- 2012year
Short summary
This note provides a simple approach to estimate the $O(1/n)$ convergence rate of the Douglas–Rachford ADM scheme, also discussing its linearized version (split inexact Uzawa method).
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Key points
- Presents a simple approach for estimating the convergence rate of the Douglas–Rachford ADM.
- The estimated convergence rate is $O(1/n)$ in terms of the iteration number.
- Discusses the linearized version of the ADM, referred to as the split inexact Uzawa method.
AI-generated from the title and abstract; the full text is not read.
Abstract
Alternating direction methods (ADMs) have been well studied in the literature, and they have found many efficient applications in various fields. In this note, we focus on the Douglas–Rachford ADM scheme proposed by Glowinski and Marrocco, and we aim at providing a simple approach to estimating its convergence rate in terms of the iteration number. The linearized version of this ADM scheme, which is known as the split inexact Uzawa method in the image processing literature, is also discussed.
The authors' abstract, as published at the source. SIAM Journal on Numerical Analysis, 2012 · DOI ↗
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Field: Computational Mechanics
Computational MechanicsEngineering