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Advances in Geometric Programming

  • Mordecai Avriel

Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 21)

Table of contents

  1. Front Matter
    Pages i-x
  2. M. Avriel
    Pages 1-4
  3. E. L. Peterson
    Pages 31-94
  4. G. Lidor, D. J. Wilde
    Pages 183-202
  5. M. Avriel, R. Dembo, U. Passy
    Pages 203-226
  6. P. V. L. N. Sarma, X. M. Martens, G. V. Reklaitis, M. J. Rijckaert
    Pages 263-281
  7. M. J. Rijckaert, X. M. Martens
    Pages 283-320
  8. M. Ratner, L. S. Lasdon, A. Jain
    Pages 321-332
  9. J. G. Ecker, W. Gochet, Y. Smeers
    Pages 343-353
  10. L. J. Mancini, D. J. Wilde
    Pages 375-387
  11. L. J. Mancini, D. J. Wilde
    Pages 389-405
  12. M. Avriel, J. D. Barrett
    Pages 407-419
  13. M. J. Rijckaert, X. M. Martens
    Pages 441-453
  14. Back Matter
    Pages 455-460

About this book

Introduction

In 1961, C. Zener, then Director of Science at Westinghouse Corpora­ tion, and a member of the U. S. National Academy of Sciences who has made important contributions to physics and engineering, published a short article in the Proceedings of the National Academy of Sciences entitled" A Mathe­ matical Aid in Optimizing Engineering Design. " In this article Zener considered the problem of finding an optimal engineering design that can often be expressed as the problem of minimizing a numerical cost function, termed a "generalized polynomial," consisting of a sum of terms, where each term is a product of a positive constant and the design variables, raised to arbitrary powers. He observed that if the number of terms exceeds the number of variables by one, the optimal values of the design variables can be easily found by solving a set of linear equations. Furthermore, certain invariances of the relative contribution of each term to the total cost can be deduced. The mathematical intricacies in Zener's method soon raised the curiosity of R. J. Duffin, the distinguished mathematician from Carnegie­ Mellon University who joined forces with Zener in laying the rigorous mathematical foundations of optimizing generalized polynomials. Interes­ tingly, the investigation of optimality conditions and properties of the optimal solutions in such problems were carried out by Duffin and Zener with the aid of inequalities, rather than the more common approach of the Kuhn-Tucker theory.

Keywords

Mathematica Variance constant design equation function programming set university variable

Editors and affiliations

  • Mordecai Avriel
    • 1
  1. 1.Technion-Israel Institute of TechnologyHaifaIsrael

Bibliographic information