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Splitting Algorithms, Modern Operator Theory, and Applications

  • Heinz H. Bauschke
  • Regina S. Burachik
  • D. Russell Luke
Book

Table of contents

  1. Front Matter
    Pages i-xix
  2. Heinz H. Bauschke, Regina S. Burachik, C. Yalçın Kaya
    Pages 45-68
  3. Radu Ioan Boţ, Ernö Robert Csetnek, Dennis Meier
    Pages 91-112
  4. Christian Clason, Barbara Kaltenbacher, Elena Resmerita
    Pages 113-135
  5. Aris Danillidis, D. Russell Luke, Matthew Tam
    Pages 137-152
  6. Asen L. Dontchev
    Pages 153-163
  7. Juan Enrique Martínez-Legaz, Dominikus Noll, Wilfredo Sosa
    Pages 309-329
  8. Walaa M. Moursi, Yuriy Zinchenko
    Pages 331-349
  9. Stephen Simons
    Pages 351-362
  10. Andreas Themelis, Masoud Ahookhosh, Panagiotis Patrinos
    Pages 363-412

About this book

Introduction

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.

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

Editors and affiliations

  • Heinz H. Bauschke
    • 1
  • Regina S. Burachik
    • 2
  • D. Russell Luke
    • 3
  1. 1.Department of MathematicsUniversity of British ColumbiaKelownaCanada
  2. 2.School of IT & Mathematical SciencesUniversity of South AustraliaMawson LakesAustralia
  3. 3.Inst. Numerische & Angewandte MathematikUniversität GöttingenGöttingenGermany

Bibliographic information