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Lectures on Mathematical Theory of Extremum Problems

  • Authors
  • Igor Vladimirovich Girsanov
  • B. T. Poljak

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 67)

Table of contents

  1. Front Matter
    Pages i-v
  2. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 1-1
  3. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 2-10
  4. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 11-20
  5. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 21-24
  6. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 25-29
  7. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 30-37
  8. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 38-42
  9. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 43-57
  10. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 58-60
  11. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 61-68
  12. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 69-77
  13. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 78-82
  14. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 83-92
  15. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 93-104
  16. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 105-113
  17. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 114-120
  18. Igor Vladimirovich Girsanov, B. T. Poljak
    Pages 121-123
  19. Back Matter
    Pages 124-137

About this book

Introduction

The author of this book, Igor' Vladimirovich Girsanov, was one of the first mathematicians to study general extremum problems and to realize the feasibility and desirability of a unified theory of extremal problems, based on a functional­ analytic approach. He actively advocated this view, and his special course, given at the Faculty of Mechanics and Mathematics of the Moscow State University in 1963 and 1964, was apparently the first systematic exposition of a unified approach to the theory of extremal problems. This approach was based on the ideas of Dubovitskii and Milyutin [1]. The general theory of extremal problems has developed so intensely during the past few years that its basic concepts may now be considered finalized. Nevertheless, as yet the basic results of this new field of mathematics have not been presented in a form accessible to a wide range of readers. (The profound paper of Dubovitskii and Milyutin [2] can hardly be recommended for a first study of the theory, since, in particular, it does not contain proofs of the fundamental theorems. ) Girsanov's book fills this gap. It contains a systematic exposition of the general principles underlying the derivation of necessary and sufficient conditions for an extremum, in a wide variety of problems. Numerous applications are given to specific extremal problems. The main material is preceded by an introductory section in which all prerequisites from functional analysis are presented.

Keywords

Calculation Extremum Lie Topology equation extrema functional analysis maximum minimum theorem

Editors and affiliations

  • B. T. Poljak
    • 1
  1. 1.Computer CenterMoscow State UniversityMoscowUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-80684-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1972
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-05857-1
  • Online ISBN 978-3-642-80684-1
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site
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