Splitting Methods in Communication, Imaging, Science, and Engineering

Front Matter....Pages i-xviii
Introduction....Pages 1-17
Some Facts About Operator-Splitting and Alternating Direction Methods....Pages 19-94
Operator Splitting....Pages 95-114
Convergence Rate Analysis of Several Splitting Schemes....Pages 115-163
Self Equivalence of the Alternating Direction Method of Multipliers....Pages 165-194
Application of the Strictly Contractive Peaceman-Rachford Splitting Method to Multi-Block Separable Convex Programming....Pages 195-235
Nonconvex Sparse Regularization and Splitting Algorithms....Pages 237-249
ADMM and Non-convex Variational Problems....Pages 251-299
Operator Splitting Methods in Compressive Sensing and Sparse Approximation....Pages 301-343
First Order Algorithms in Variational Image Processing....Pages 345-407
A Parameter Free ADI-Like Method for the Numerical Solution of Large Scale Lyapunov Equations....Pages 409-425
Splitting Enables Overcoming the Curse of Dimensionality....Pages 427-432
ADMM Algorithmic Regularization Paths for Sparse Statistical Machine Learning....Pages 433-459
Decentralized Learning for Wireless Communications and Networking....Pages 461-497
Splitting Methods for SPDEs: From Robustness to Financial Engineering, Optimal Control, and Nonlinear Filtering....Pages 499-539
Application of Operator Splitting Methods in Finance....Pages 541-575
A Numerical Method to Solve Multi-Marginal Optimal Transport Problems with Coulomb Cost....Pages 577-601
Robust Split-Step Fourier Methods for Simulating the Propagation of Ultra-Short Pulses in Single- and Two-Mode Optical Communication Fibers....Pages 603-625
Operator Splitting Methods with Error Estimator and Adaptive Time-Stepping. Application to the Simulation of Combustion Phenomena....Pages 627-641
Splitting Methods for Some Nonlinear Wave Problems....Pages 643-676
Operator Splitting Algorithms for Free Surface Flows: Application to Extrusion Processes....Pages 677-729
An Operator Splitting Approach to the Solution of Fluid-Structure Interaction Problems in Hemodynamics....Pages 731-772
On Circular Cluster Formation in a Rotating Suspension of Non-Brownian Settling Particles in a Fully Filled Circular Cylinder: An Operator Splitting Approach to the Numerical Simulation....Pages 773-801
Back Matter....Pages 803-820