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Convex Optimization with Computational Errors

  • Alexander J. Zaslavski
Book
  • 1.5k Downloads

Part of the Springer Optimization and Its Applications book series (SOIA, volume 155)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Alexander J. Zaslavski
    Pages 1-24
  3. Alexander J. Zaslavski
    Pages 25-81
  4. Alexander J. Zaslavski
    Pages 83-125
  5. Alexander J. Zaslavski
    Pages 127-150
  6. Alexander J. Zaslavski
    Pages 151-171
  7. Alexander J. Zaslavski
    Pages 173-241
  8. Alexander J. Zaslavski
    Pages 259-275
  9. Alexander J. Zaslavski
    Pages 277-286
  10. Alexander J. Zaslavski
    Pages 287-293
  11. Alexander J. Zaslavski
    Pages 295-320
  12. Alexander J. Zaslavski
    Pages 321-354
  13. Back Matter
    Pages 355-360

About this book

Introduction

This book studies approximate solutions of optimization problems in the presence of computational errors. It contains a number of results on the convergence behavior of algorithms in a Hilbert space, which are well known as important tools for solving optimization problems. The research presented continues from the author's (c) 2016 book Numerical Optimization with Computational Errors. Both books study algorithms taking into account computational errors which are always present in practice. The main goal is, for a known computational error, to obtain the approximate solution and the number of iterations needed. 

The discussion takes into consideration that for every algorithm, its iteration consists of several steps; computational errors for various steps are generally different. This fact, which was not accounted for in the previous book, is indeed important in practice. For example, the subgradient projection algorithm consists of two steps—a calculation of a subgradient of the objective function and a  calculation of a projection on the feasible set. In each of these two steps there is a computational error and these two computational errors are generally different. 

The book is of interest for researchers and engineers working in optimization. It also can be useful in preparation courses for graduate students.  The main feature of the book will appeal specifically to researchers and engineers working in optimization as well as to experts in applications of optimization to engineering and economics.

Keywords

convex optimization mathematical programming computational error nonlinear analysis solving real-world optimization problems subgradient projection algorithm mirror descent algorithm smooth objective function gradient algorithm nonsmooth problems convex functions composite objective function

Authors and affiliations

  • Alexander J. Zaslavski
    • 1
  1. 1.Department of Mathematics Amado BuildingIsrael Institute of TechnologyHaifaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-37822-6
  • Copyright Information Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-37821-9
  • Online ISBN 978-3-030-37822-6
  • Series Print ISSN 1931-6828
  • Series Online ISSN 1931-6836
  • Buy this book on publisher's site