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  • © 2019

Splitting Algorithms, Modern Operator Theory, and Applications

Editors:

  1. Heinz H. Bauschke

    1. Department of Mathematics, University of British Columbia, Kelowna, Canada

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  2. Regina S. Burachik

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

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    You can also search for this editor in PubMed   Google Scholar

  3. D. Russell Luke

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

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Brings together research articles and state-of-the-art surveys in broad areas of optimization and numerical analysis

  • Theory and applications are presented in novel and insightful ways

  • Focuses on algorithms, advances in monotone operator theory, topics from variational analysis and nonsmooth optimization

  • Dedicated to Jonathan M. Borwein, one of the most versatile mathematicians in contemporary history

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xix
    PDF

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

    • Heinz H. Bauschke, Regina S. Burachik, C. Yalçın Kaya
    Pages 45-68

  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

  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
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About this book

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.
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Keywords

  • 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
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Editors and Affiliations

  • 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

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About the editors

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.
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Bibliographic Information

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Access via your institution
eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-3-030-25939-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 84.99
Price excludes VAT (USA)
Hardcover Book USD 119.99
Price excludes VAT (USA)
Learn about institutional subscriptions