Optimization—Theory and Applications

Problems with Ordinary Differential Equations

  • Lamberto Cesari

Part of the Applications of Mathematics book series (SMAP, volume 17)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Lamberto Cesari
    Pages 1-23
  3. Lamberto Cesari
    Pages 116-158
  4. Lamberto Cesari
    Pages 206-232
  5. Lamberto Cesari
    Pages 430-442
  6. Back Matter
    Pages 523-542

About this book

Introduction

This book has grown out of lectures and courses in calculus of variations and optimization taught for many years at the University of Michigan to graduate students at various stages of their careers, and always to a mixed audience of students in mathematics and engineering. It attempts to present a balanced view of the subject, giving some emphasis to its connections with the classical theory and to a number of those problems of economics and engineering which have motivated so many of the present developments, as well as presenting aspects of the current theory, particularly value theory and existence theorems. However, the presentation ofthe theory is connected to and accompanied by many concrete problems of optimization, classical and modern, some more technical and some less so, some discussed in detail and some only sketched or proposed as exercises. No single part of the subject (such as the existence theorems, or the more traditional approach based on necessary conditions and on sufficient conditions, or the more recent one based on value function theory) can give a sufficient representation of the whole subject. This holds particularly for the existence theorems, some of which have been conceived to apply to certain large classes of problems of optimization. For all these reasons it is essential to present many examples (Chapters 3 and 6) before the existence theorems (Chapters 9 and 11-16), and to investigate these examples by means of the usual necessary conditions, sufficient conditions, and value function theory.

Keywords

Maxima Optimale Regelung Reentry Variationsrechnung optimal control optimization

Authors and affiliations

  • Lamberto Cesari
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8165-5
  • Copyright Information Springer-Verlag New York 1983
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-8167-9
  • Online ISBN 978-1-4613-8165-5
  • Series Print ISSN 0172-4568
  • About this book