Splitting Methods in Communication, Imaging, Science, and Engineering

1. Front Matter

   Pages i-xviii

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2. Introduction

   • Roland Glowinski, Stanley J. Osher, Wotao Yin

   Pages 1-17

3. Some Facts About Operator-Splitting and Alternating Direction Methods

   • Roland Glowinski, Tsorng-Whay Pan, Xue-Cheng Tai

   Pages 19-94

4. Operator Splitting

   • Shev MacNamara, Gilbert Strang

   Pages 95-114

5. Convergence Rate Analysis of Several Splitting Schemes

   • Damek Davis, Wotao Yin

   Pages 115-163

6. Self Equivalence of the Alternating Direction Method of Multipliers

   • Ming Yan, Wotao Yin

   Pages 165-194

7. Application of the Strictly Contractive Peaceman-Rachford Splitting Method to Multi-Block Separable Convex Programming

   • Bingsheng He, Han Liu, Juwei Lu, Xiaoming Yuan

   Pages 195-235

8. Nonconvex Sparse Regularization and Splitting Algorithms

   • Rick Chartrand, Wotao Yin

   Pages 237-249

9. ADMM and Non-convex Variational Problems

   • Roland Glowinski

   Pages 251-299

10. Operator Splitting Methods in Compressive Sensing and Sparse Approximation

    • Tom Goldstein, Xiaoqun Zhang

    Pages 301-343

11. First Order Algorithms in Variational Image Processing

    • M. Burger, A. Sawatzky, G. Steidl

    Pages 345-407

12. A Parameter Free ADI-Like Method for the Numerical Solution of Large Scale Lyapunov Equations

    • Danny C. Sorensen

    Pages 409-425

13. Splitting Enables Overcoming the Curse of Dimensionality

    • Jérôme Darbon, Stanley J. Osher

    Pages 427-432

14. ADMM Algorithmic Regularization Paths for Sparse Statistical Machine Learning

    • Yue Hu, Eric C. Chi, Genevera I. Allen

    Pages 433-459

15. Decentralized Learning for Wireless Communications and Networking

    • Georgios B. Giannakis, Qing Ling, Gonzalo Mateos, Ioannis D. Schizas, Hao Zhu

    Pages 461-497

16. Splitting Methods for SPDEs: From Robustness to Financial Engineering, Optimal Control, and Nonlinear Filtering

    • Christian Bayer, Harald Oberhauser

    Pages 499-539

17. Application of Operator Splitting Methods in Finance

    • Karel in’t Hout, Jari Toivanen

    Pages 541-575

18. A Numerical Method to Solve Multi-Marginal Optimal Transport Problems with Coulomb Cost

    • Jean-David Benamou, Guillaume Carlier, Luca Nenna

    Pages 577-601

19. Robust Split-Step Fourier Methods for Simulating the Propagation of Ultra-Short Pulses in Single- and Two-Mode Optical Communication Fibers

    • Ralf Deiterding, Stephen W. Poole

    Pages 603-625

20. Operator Splitting Methods with Error Estimator and Adaptive Time-Stepping. Application to the Simulation of Combustion Phenomena

    • Stéphane Descombes, Max Duarte, Marc Massot

    Pages 627-641

This book is about computational methods based on operator splitting.   It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas.  

• Operator Splitting Methods
• Alternating Direction Method of Multipliers
• Bregman Methods
• Large-scale Optimization
• Scientific Computing

• Department of Mathematics, University of Houston, Houston, USA

  Roland Glowinski

• Department of Mathematics, UCLA, Los Angeles, USA

  Stanley J. Osher, Wotao Yin

Roland Glowinski works in Computational Mechanics and Physics and more generally in areas involving the numerical solution of partial differential equations and inequalities. Stanley Osher is a Professor of Mathematics, Computer Science and Electrical Engineering at UCLA, and is an Associate Director of the NSF funded Institute for Pure and Applied Mathematics. Wotao Yin works in optimization theory, develops many fast algorithms for compressive sensing, image processing, medical imaging, wireless networking, etc.