Splitting Methods in Communication, Imaging, Science, and Engineering

Introduction.- Some Facts about Operator-Splitting and Alternating Direction Methods.- Operator Splitting.- Convergence Rate Analysis of Several Splitting Schemes.- Self Equivalence of the Alternating Direction Method of Multipliers.- Application of the Strictly Contractive Peaceman-Rachford Splitting Method to Multi-block Separable Convex Programming.- Nonconvex Sparse Regularization and Splitting Algorithms.- ADMM and Non-convex Variational Problems.- Operator Splitting Methods in Compressive Sensing and Sparse Approximation.- First Order Algorithms in Variational Image Processing.- A Parameter Free ADI-like Method for the Numerical Solution of Large Scale Lyapunov Equations.- Splitting Enables Overcoming the Curse of Dimensionality.- ADMM Algorithmic Regularization Paths for Sparse Statistical Machine Learning.- Decentralized Learning for Wireless Communications and Networking.- Splitting Methods for SPDEs: From Robustness to Financial Engineering, Optimal Control and Nonlinear Filtering.- Application of Operator Splitting Methods in Finance.- A Numerical Method to Solve Multi-marginal Optimal Transport Problems with Coulomb Cost.- Robust Split-step Fourier Methods for Simulating the Propagation of Ultra-short Pulses in Single- and Two-mode Optical Communication Fibers.- Operator Splitting Methods with Error Estimator and Adaptive Time-stepping: Application to the Simulation of Combustion Phenomena.- Operator Splitting Algorithms for Free Surface Flows: Application to Extrusion Processes.- An Operator Splitting Approach to the Solution of Fluid-structure Interaction Problems with Hemodynamics.- 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.