Splitting Algorithms, Modern Operator Theory, and Applications

1. Front Matter

   Pages i-xix

   PDF

2. Convergence Rate of Proximal Inertial Algorithms Associated with Moreau Envelopes of Convex Functions

   • Hedy Attouch, Juan Peypouquet

   Pages 1-44

3. Constraint Splitting and Projection Methods for Optimal Control of Double Integrator

   • Heinz H. Bauschke, Regina S. Burachik, C. Yalçın Kaya

   Pages 45-68

4. Numerical Explorations of Feasibility Algorithms for Finding Points in the Intersection of Finite Sets

   • Heinz H. Bauschke, Sylvain Gretchko, Walaa M. Moursi

   Pages 69-90

5. Variable Metric ADMM for Solving Variational Inequalities with Monotone Operators over Affine Sets

   • Radu Ioan Boţ, Ernö Robert Csetnek, Dennis Meier

   Pages 91-112

6. Regularization of Ill-Posed Problems with Non-negative Solutions

   • Christian Clason, Barbara Kaltenbacher, Elena Resmerita

   Pages 113-135

7. Characterizations of Super-Regularity and Its Variants

   • Aris Danillidis, D. Russell Luke, Matthew Tam

   Pages 137-152

8. The Inverse Function Theorems of L. M. Graves

   • Asen L. Dontchev

   Pages 153-163

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

   • Xiaoling Fu, Bingsheng He, Xiangfeng Wang, Xiaoming Yuan

   Pages 165-226

10. Variable Metric Algorithms Driven by Averaged Operators

    • Lilian E. Glaudin

    Pages 227-242

11. A Glimpse at Pointwise Asymptotic Stability for Continuous-Time and Discrete-Time Dynamics

    • Rafal Goebel

    Pages 243-267

12. A Survey on Proximal Point Type Algorithms for Solving Vector Optimization Problems

    • Sorin-Mihai Grad

    Pages 269-308

13. Non-polyhedral Extensions of the Frank and Wolfe Theorem

    • Juan Enrique Martínez-Legaz, Dominikus Noll, Wilfredo Sosa

    Pages 309-329

14. A Note on the Equivalence of Operator Splitting Methods

    • Walaa M. Moursi, Yuriy Zinchenko

    Pages 331-349

15. Quasidensity: A Survey and Some Examples

    • Stephen Simons

    Pages 351-362

16. On the Acceleration of Forward-Backward Splitting via an Inexact Newton Method

    • Andreas Themelis, Masoud Ahookhosh, Panagiotis Patrinos

    Pages 363-412

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

    • Isao Yamada, Masao Yamagishi

    Pages 413-489

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 optimization, especially as they pertain to algorithms and concrete, implementable methods.   The theory of monotone operators is a central framework for understanding and analyzing splitting algorithms. Topics discussed in the volume were presented at the interdisciplinary workshop titled Splitting Algorithms, Modern Operator Theory, and Applications held in Oaxaca, Mexico in September, 2017. Dedicated to Jonathan M. Borwein, one of the most versatile mathematicians in contemporary history, this compilation brings theory together with applications in novel and insightful ways.

• operator splitting methods
• monotone operators and optimization algortihms
• monotone operators
• quantification of convergence rates
• splitting algorithms
• monotone operator theory
• variational problems
• decomposition and operator splitting
• optimization algorithms
• Dykstra projection method
• dedicated to Jonathan Borwein
• optimal control
• Moreau envelopes
• ADMM
• ill-posed problems
• inverse function theorem
• Gaussian back substitution
• variable metric algorithms
• discrete-time dyanamics
• vector optimization problem

• Department of Mathematics, University of British Columbia, Kelowna, Canada

  Heinz H. Bauschke

• School of IT & Mathematical Sciences, University of South Australia, Mawson Lakes, Australia

  Regina S. Burachik

• Inst. Numerische & Angewandte Mathematik, Universität Göttingen, Göttingen, Germany

  D. Russell Luke

Heinz H. Bauschke is a Full Professor of Mathematics at the University of British Columbia (Okanagan campus). His main research interests are in convex analysis and optimization, monotone operator theory, projection methods, and applications. He has authored or co-authored more than 125 refereed publications, including 1 book, and co-edited several conference proceedings with Springer.


Regina S. Burachik is an associate professor in the School of Information Technology and Mathematical Sciences at the University of South Australia (UniSA). Regina’s research focuses on several aspects of optimization, ranging from functional analysis and variational inequalities to practical applications. She publishes in optimization theory, solution techniques for nonsmooth optimization, and convergence analysis of algorithms. Regina has published more than 60 journal articles and co-authored a Springer book with A.N. Iusem.


D. Russell Luke is professor of continuous optimization at the Institute for Numerical and Applied Mathematics at the Georg-August University of Göttingen where he leads the workgroup in continuous optimization and variational analysis. Prof.  Luke  has published over fifty refereed journal  articles and proceedings and is co-author of one book.  This is his second edited volume with Springer.

Policies and ethics