Splitting Algorithms, Modern Operator Theory, and Applications

• Corporate Author: SpringerLink (Online service)
• Other Authors: Bauschke, Heinz H. (Editor, http://id.loc.gov/vocabulary/relators/edt), Burachik, Regina S. (Editor, http://id.loc.gov/vocabulary/relators/edt), Luke, D. Russell (Editor, http://id.loc.gov/vocabulary/relators/edt)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Subjects: Operator theory.; Calculus of variations.; Partial differential equations.; Functional analysis.; Numerical analysis.; Operator Theory.; Calculus of Variations and Optimal Control; Optimization.; Partial Differential Equations.; Functional Analysis.; Numerical Analysis.

This book brings together research articles and state-of-the-art surveys in broad areas of optimization and numerical analysis with particular emphasis on algorithms. The discussion also focuses on advances in monotone operator theory and other topics from variational analysis and nonsmooth optimiza...

Table of Contents:

• 1. Convergence Rate of Proximal Inertial Algorithms Associated with Moreau Envelopes of Convex Functions (H. Attouch, J. Peypouquet)
• 2. Constraint Splitting and Projection Methods for Optimal Control of Double Integrator (H.H. Bauschke, R.S. Burachik, C.Y. Kaya)
• 3. Numerical Explorations of Feasibility Algorithms for Finding Points in the Intersection of Finite Sets (H.,H. Bauschke, S. Gretchko, W.M. Moursi)
• 4. Variable Metric ADMM for Solving Variational Inequalities with Monotone Operators Over Affine Sets (R. I. Bot, E.R. Csetnek, D. Meier)
• 5. Regularization of Ill-posed Problems with Non-Negative Solutions (C. Clason, B. Kaltenbacher, E. Resmerita)
• 6. Characterizations of Super-regularity and its Variants (A. Danillidis, D.R. Luke, M. Tam)
• 7. The Inverse Function Theorems of L.M. Graves (A.L. Dontchev)
• 8. Block-wise Alternating Direction Method of Multipliers with Gaussian Back Substitution for Multiple-block Convex Programming (X. Fu, B. He, X. Wang, X. Yuan)
• 9. Variable Metric Algorithms Driven by Averaged Operations (L.E. Glaudin)
• 10. A Glimpse at Pointwise Asymptotic Stability for Continuous-time and Discrete-time Dynamics (R. Goebel)
• 11. A Survey on Proximal Point Type Algorithms for Solving Vector Optimization Problems (S-M Grad)
• 12. Non-polyhedral Extensions of the Frank and Wolfe Theorem (J.E. Martínez-Legaz, D. Noll, W. Sosa)
• 13. A Note on the Equivalence of Operator Splitting Methods (W.M. Moursi, Y. Zinchenko)
• 14. Quasidensity: A Survey and Some Examples (S. Simons)
• 15. On the Acceleration of Forward-Backward Splitting via an Inexact Newton Method (A. Themelis, M. Ahookosh, P. Patrinos)
• 16. Hierarchical Convex Optimization by the Hybrid Steepest Descent Method with Proximal Splitting Operators - Enhancements of SVM and Lasso (I. Yamada, M. Yamagishi)
• Appendix
• References.