Splitting Algorithms, Modern Operator Theory, and Applications

Chapter 1 Convergence Rate of Proximal Inertial Algorithms Associated with Moreau Envelopes of Convex Functions

Chapter 3 Numerical Explorations of Feasibility Algorithms for Finding Points in the Intersection of Finite Sets

Chapter 4 Variable Metric ADMM for Solving Variational Inequalities with Monotone Operators over Affine Sets

Chapter 5 Regularization of Ill-Posed Problems with Non-negative Solutions

Chapter 6 Characterizations of Super-Regularity and Its Variants

Chapter 7 The Inverse Function Theorems of L. M. Graves

Chapter 8 Block-Wise Alternating Direction Method of Multipliers with Gaussian Back Substitution for Multiple-Block Convex Programming

Chapter 9 Variable Metric Algorithms Driven by Averaged Operators

Chapter 10 A Glimpse at Pointwise Asymptotic Stability for Continuous-Time and Discrete-Time Dynamics

Chapter 11 A Survey on Proximal Point Type Algorithms for Solving Vector Optimization Problems

Chapter 12 Non-polyhedral Extensions of the Frank and Wolfe Theorem

Chapter 13 A Note on the Equivalence of Operator Splitting Methods

Chapter 14 Quasidensity: A Survey and Some Examples

Chapter 15 On the Acceleration of Forward-Backward Splitting via an Inexact Newton Method

Chapter 16 Hierarchical Convex Optimization by the Hybrid Steepest Descent Method with Proximal Splitting Operators—Enhancements of SVM and Lasso