Optimization Methods

  • Henning Tolle

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Henning Tolle
    Pages 1-34
  3. Henning Tolle
    Pages 35-107
  4. Henning Tolle
    Pages 108-193
  5. Back Matter
    Pages 194-226

About this book

Introduction

Variational problems which are interesting from physical and technical viewpoints are often supplemented with ordinary differential equations as constraints, e. g. , in the form of Newton's equations of motion. Since analytical solutions for such problems are possible only in exceptional cases and numerical treat­ ment of extensive systems of differential equations formerly caused computational difficulties, in the classical calculus of variations these problems have generally been considered only with respect to their theoretical aspects. However, the advent of digital computer installations has enabled us, approximately since 1950, to make more practical use of the formulas provided by the calculus of variations, and also to proceed from relationships which are oriented more numerically than analytically. This has proved very fruitful since there are areas, in particular, in automatic control and space flight technology, where occasionally even relatively small optimization gains are of interest. Further on, if in a problem we have a free function of time which we may choose as advantageously as possible, then determination of the absolutely optimal course of this function appears always advisable, even if it gives only small improve­ ments or if it leads to technical difficulties, since: i) we must in any case choose some course for free functions; a criterion which gives an optimal course for that is very practical ii) also, when choosing a certain technically advantageous course we mostly want to know to which extent the performance of the system can further be increased by variation of the free function.

Keywords

Optimization Planungsrechnung Variationsrechnung calculus differential equation equation function

Authors and affiliations

  • Henning Tolle
    • 1
  1. 1.Fachgebiet RegelsystemstheorieTechnische Hochschule Darmstadt61 DarmstadtWest Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-87731-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1975
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-07194-5
  • Online ISBN 978-3-642-87731-5
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book