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Extrema of Smooth Functions

With Examples from Economic Theory

  • Mohamed Ali El-Hodiri

Table of contents

  1. Front Matter
    Pages I-XII
  2. Finite Dimensional Problems

    1. Front Matter
      Pages 1-1
    2. Mohamed Ali El-Hodiri
      Pages 3-22
    3. Mohamed Ali El-Hodiri
      Pages 23-46
    4. Mohamed Ali El-Hodiri
      Pages 47-53
    5. Mohamed Ali El-Hodiri
      Pages 54-91
  3. Variational Problems

    1. Front Matter
      Pages 93-93
    2. Mohamed Ali El-Hodiri
      Pages 95-127
    3. Mohamed Ali El-Hodiri
      Pages 128-134
    4. Mohamed Ali El-Hodiri
      Pages 135-162
  4. Back Matter
    Pages 163-197

About this book

Introduction

It is not an exaggeration to state that most problems dealt with in economic theory can be formulated as problems in optimization theory. This holds true for the paradigm of "behavioral" optimization in the pursuit of individual self interests and societally efficient resource allocation, as well as for equilibrium paradigms where existence and stability problems in dynamics can often be stated as "potential" problems in optimization. For this reason, books in mathematical economics and in mathematics for economists devote considerable attention to optimization theory. However, with very few exceptions, the reader who is interested in further study is left with the impression that there is no further place to go to and that what is in these second hand sources is all these is available as far as the subject of optimization theory is concerned. On the other hand the main results from mathematics are often carelessly stated or, more often than not, they do not get to be formally stated at all. Furthermore, it should be well understood that economic theory in general and, mathematical economics in particular, must be classified as special types of applied mathematics or, more precisely, of motivated mathematics since tools of mathematical analysis are used to prove theorems in an economics context in the manner in which probability theory may be classified. Hence, rigor and correct scholarship are of utmost importance and can not be subject to compromise.

Keywords

Calculus of Variations Infinitesimalrechnung Optimierungstheorie Variationsrechnung control theory economics mathematical programming optimal control optimization optimization theory

Authors and affiliations

  • Mohamed Ali El-Hodiri
    • 1
  1. 1.Department of EconomicsUniversity of KansasLawrenceUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-76793-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-76795-1
  • Online ISBN 978-3-642-76793-7
  • Buy this book on publisher's site
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