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Some Facts About Operator-Splitting and Alternating Direction Methods

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Splitting Methods in Communication, Imaging, Science, and Engineering

Part of the book series: Scientific Computation ((SCIENTCOMP))

Abstract

The main goal of this chapter is to give the reader a (relatively) brief overview of operator-splitting, augmented Lagrangian and ADMM methods and algorithms. Following a general introduction to these methods, we will give several applications in Computational Fluid Dynamics, Computational Physics, and Imaging. These applications will show the flexibility, modularity, robustness, and versatility of these methods. Some of these applications will be illustrated by the results of numerical experiments; they will confirm the capabilities of operator-splitting methods concerning the solution of problems still considered complicated by today standards.

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  1. Department of Mathematics, University of Houston, Houston, TX, 77204, USA

    Roland Glowinski & Tsorng-Whay Pan

  2. Department of Mathematics, University of Bergen, Bergen, Norway

    Xue-Cheng Tai

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    Roland Glowinski

  2. Department of Mathematics, UCLA, Los Angeles, California, USA

    Stanley J. Osher

  3. Department of Mathematics, UCLA, Los Angeles, California, USA

    Wotao Yin

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Glowinski, R., Pan, TW., Tai, XC. (2016). Some Facts About Operator-Splitting and Alternating Direction Methods. In: Glowinski, R., Osher, S., Yin, W. (eds) Splitting Methods in Communication, Imaging, Science, and Engineering. Scientific Computation. Springer, Cham. https://doi.org/10.1007/978-3-319-41589-5_2

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