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Newton-Type Methods for Optimization and Variational Problems

  • Alexey F. Izmailov
  • Mikhail V. Solodov

Table of contents

  1. Front Matter
    Pages i-xix
  2. Alexey F. Izmailov, Mikhail V. Solodov
    Pages 1-60
  3. Alexey F. Izmailov, Mikhail V. Solodov
    Pages 61-137
  4. Alexey F. Izmailov, Mikhail V. Solodov
    Pages 139-203
  5. Alexey F. Izmailov, Mikhail V. Solodov
    Pages 205-303
  6. Alexey F. Izmailov, Mikhail V. Solodov
    Pages 305-366
  7. Alexey F. Izmailov, Mikhail V. Solodov
    Pages 367-437
  8. Alexey F. Izmailov, Mikhail V. Solodov
    Pages 439-541
  9. Back Matter
    Pages 543-573

About this book

Introduction

This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis.

Keywords

Complementarity problems Newton method Optimization Sequential quadratic programming Variational problems

Authors and affiliations

  • Alexey F. Izmailov
    • 1
  • Mikhail V. Solodov
    • 2
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Instituto de Matem´atica Pura e AplicadaRio de JaneiroBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-04247-3
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-04246-6
  • Online ISBN 978-3-319-04247-3
  • Series Print ISSN 1431-8598
  • Series Online ISSN 2197-1773
  • Buy this book on publisher's site