Splitting Algorithms, Modern Operator Theory, and Applications

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.

Auteur
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.

Contenu

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.