Fixed-Point Algorithms for Inverse Problems in Science and Engineering

  • Heinz H. Bauschke
  • Regina S. Burachik
  • Patrick L. Combettes
  • Veit Elser
  • D. Russell Luke
  • Henry Wolkowicz

Part of the Springer Optimization and Its Applications book series (SOIA, volume 49)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Heinz H. Bauschke, Sarah M. Moffat, Xianfu Wang
    Pages 23-32
  3. Jonathan M. Borwein, D. Russell Luke
    Pages 65-92
  4. Jonathan M. Borwein, Brailey Sims
    Pages 93-109
  5. Radu Ioan Boţ, Ernö Robert Csetnek
    Pages 111-130
  6. Jérôme Boulanger, Peter Elbau, Carsten Pontow, Otmar Scherzer
    Pages 131-154
  7. Andrzej Cegielski, Yair Censor
    Pages 155-183
  8. Patrick L. Combettes, Jean-Christophe Pesquet
    Pages 185-212
  9. Bryan Gardiner, Yves Lucet
    Pages 243-259
  10. Genaro López, Victoria Martín-Márquez
    Pages 273-299

About this book

Introduction

 

Fixed-Point Algorithms for Inverse Problems in Science and Engineering presents some of the most recent work from leading researchers in variational and numerical analysis.  The contributions in this collection provide state-of-the-art theory and practice in first-order fixed-point algorithms, identify emerging problems driven by applications, and discuss new approaches for solving these problems.

 

This book is a compendium of topics explored at the Banff International Research Station “Interdisciplinary Workshop on Fixed-Point Algorithms for Inverse Problems in Science and Engineering”  in November of 2009.  The workshop included a broad range of research including variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry.

 

Key topics and features of this book include:

·         Theory of Fixed-point algorithms: variational analysis, convex analysis, convex and nonconvex  optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory

·         Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods

·         Applications:  Image and signal processing, antenna optimization, location problems

 

The wide scope of applications presented in this volume easily serve as a basis for new and innovative research and collaboration.

Keywords

Fixed-point algorithms Inverse problems Numerical analysis

Editors and affiliations

  • Heinz H. Bauschke
    • 1
  • Regina S. Burachik
    • 2
  • Patrick L. Combettes
    • 3
  • Veit Elser
    • 4
  • D. Russell Luke
    • 5
  • Henry Wolkowicz
    • 6
  1. 1.Okanagan Campus, Department of Mathematics and StatisticUniversity of British ColumbiaKelownaCanada
  2. 2.School of Mathematics & Statistics, Division of Information TechnologyUniversity of South AustraliaMawson LakesAustralia
  3. 3.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie CurieParisFrance
  4. 4.Dept. Physics, Lab. Atomic & Solid StateCornell UniversityIthacaUSA
  5. 5.Institut für Numerische und Angewandte MUniversität GöttingenGöttingenGermany
  6. 6.Faculty of Mathematics, Dept. Combinatorics & OptimizationUniversity of WaterlooWaterlooCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-9569-8
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-9568-1
  • Online ISBN 978-1-4419-9569-8
  • Series Print ISSN 1931-6828
  • About this book
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