Constrained Extrema Introduction to the Differentiable Case with Economic Applications

1. Front Matter

   Pages i-iii

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2. Preface

   1. Preface

      • Mohamed El-Hodiri

      Pages 1-3

3. Introductory Survey

   1. Front Matter

      Pages 4-4

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   2. A Survey of Derivative Characterization of Constrained Extrema

      • Mohamed A. El-Hodiri

      Pages 5-23

4. Finite Dimensional Problems

   1. Front Matter

      Pages 24-24

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   2. Equality Constraints

      • Mohamed A. El-Hodiri

      Pages 25-33

   3. Inequalities as Added Constraints

      • Mohamed A. El-Hodiri

      Pages 34-38

   4. Extensions and Applications

      • Mohamed A. El-Hodiri

      Pages 39-59

5. Variational Problems

   1. Front Matter

      Pages 60-60

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   2. The Problem of Bolza with Equality Constraints

      • Mohamed A. El-Hodiri

      Pages 61-77

   3. The Problem of Bolza With Equality-Inequality Constraints

      • Mohamed A. El-Hodiri

      Pages 78-83

   4. Extensions and Applications

      • Mohamed A. El-Hodiri

      Pages 84-127

6. Back Matter

   Pages 128-132

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These notes are the result of an interrupted sequence of seminars on optimiza­ tion theory with economic applications starting in 1964-1965. This is mentioned by way of explaining the uneven style that pervades them. Lately I have been using the notes for a two semester course on the subject for graduate students in economics. Except for the introductory survey, the notes are intended to provide an appetizer to more sophisticated aspects of optimization theory and economic theory. The notes are divided into three parts. Part I collects most of the results on constrained extremf! of differentiable functionals on finite and not so finite dimensional spaces. It is to be used as a reference and as a place to find credits to various authors whose ideas we report. Part II is concerned with finite dimensional problems and is written in detail. Needless to say, my contributions are marginal. The economic examples are well known and are presented by way of illustrating the theory. Part III is devoted to variational problems leading to a discussion of some optimal control problems. There is a vast amount of literature on these problems and I tried to limit my intrusions to explaining some of the obvious steps that are usually left out. I have borrowed heavily from Akhiezer [ 1], Berkovitz [ 7], Bliss [lOJ and Pars [40J. The economic applications represent some of my work and are presented in the spirit of illustration.

• economic theory
• economics
• inequality
• optimal control
• optimization
• optimization theory
• rating
• value-at-risk

• Department of Economics, University of Kansas, Lawrence, USA

  Mohamed A. El-Hodiri

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