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Numerical Optimization with Computational Errors

  • Alexander J. Zaslavski

Part of the Springer Optimization and Its Applications book series (SOIA, volume 108)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Alexander J. Zaslavski
    Pages 1-9
  3. Alexander J. Zaslavski
    Pages 11-40
  4. Alexander J. Zaslavski
    Pages 41-58
  5. Alexander J. Zaslavski
    Pages 59-72
  6. Alexander J. Zaslavski
    Pages 73-84
  7. Alexander J. Zaslavski
    Pages 85-103
  8. Alexander J. Zaslavski
    Pages 105-118
  9. Alexander J. Zaslavski
    Pages 119-136
  10. Alexander J. Zaslavski
    Pages 137-147
  11. Alexander J. Zaslavski
    Pages 149-168
  12. Alexander J. Zaslavski
    Pages 205-224
  13. Alexander J. Zaslavski
    Pages 225-238
  14. Alexander J. Zaslavski
    Pages 239-264
  15. Alexander J. Zaslavski
    Pages 265-296
  16. Back Matter
    Pages 297-304

About this book

Introduction

This book studies the approximate solutions of optimization problems in the presence of computational errors. A number of results are presented on the convergence behavior of algorithms in a Hilbert space; these algorithms are examined taking into account computational errors. The author illustrates that algorithms generate a good approximate solution, if computational errors are bounded from above by a small positive constant. Known computational errors are examined with the aim of determining an approximate solution. Researchers and students interested in the optimization theory and its applications will find this book instructive and informative. 


This monograph contains 16 chapters; including a chapters devoted to the subgradient projection algorithm, the mirror descent algorithm, gradient projection algorithm, the Weiszfelds method, constrained convex minimization problems, the convergence of a proximal point method in a Hilbert space, the continuous subgradient method, penalty methods and Newton’s method.

Keywords

nonlinear programming mathematical programming proximal point methods extragradient methods continuous subgradient method

Authors and affiliations

  • Alexander J. Zaslavski
    • 1
  1. 1.Department of MathematicsThe Technion – Israel Institute of TechnHaifaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-30921-7
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-30920-0
  • Online ISBN 978-3-319-30921-7
  • Series Print ISSN 1931-6828
  • Series Online ISSN 1931-6836
  • Buy this book on publisher's site