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Advances in Geometric Programming

  • Book
  • © 1980

Overview

Editors:
  1. Mordecai Avriel

    1. Technion-Israel Institute of Technology, Haifa, Israel

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

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Table of contents (23 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Introduction

    • M. Avriel
    Pages 1-4

  3. Geometric Programming in Terms of Conjugate Functions

    • M. Hamala
    Pages 5-30

  4. Geometric Programming

    • E. L. Peterson
    Pages 31-94

  5. Optimality Conditions in Generalized Geometric Programming

    • E. L. Peterson
    Pages 95-105

  6. Saddle Points and Duality in Generalized Geometric Programming

    • E. L. Peterson
    Pages 107-133

  7. Constrained Duality via Unconstrained Duality in Generalized Geometric Programming

    • E. L. Peterson
    Pages 135-142

  8. Fenchel’s Duality Theorem in Generalized Geometric Programming

    • E. L. Peterson
    Pages 143-149

  9. Generalized Geometric Programming Applied to Problems of Optimal Control: I. Theory

    • T. R. Jefferson, C. H. Scott
    Pages 151-163

  10. Projection and Restriction Methods in Geometric Programming and Related Problems

    • R. A. Abrams, C. T. Wu
    Pages 165-182

  11. Transcendental Geometric Programs

    • G. Lidor, D. J. Wilde
    Pages 183-202

  12. Solution of Generalized Geometric Programs

    • M. Avriel, R. Dembo, U. Passy
    Pages 203-226

  13. Current State of the Art of Algorithms and Computer Software for Geometric Programming

    • R. S. Dembo
    Pages 227-261

  14. A Comparison of Computational Strategies for Geometric Programs

    • P. V. L. N. Sarma, X. M. Martens, G. V. Reklaitis, M. J. Rijckaert
    Pages 263-281

  15. Comparison of Generalized Geometric Programming Algorithms

    • M. J. Rijckaert, X. M. Martens
    Pages 283-320

  16. Solving Geometric Programs Using GRG: Results and Comparisons

    • M. Ratner, L. S. Lasdon, A. Jain
    Pages 321-332

  17. Dual to Primal Conversion in Geometric Programming

    • R. S. Dembo
    Pages 333-342

  18. A Modified Reduced Gradient Method for Dual Posynomial Programming

    • J. G. Ecker, W. Gochet, Y. Smeers
    Pages 343-353

  19. Global Solutions of Mathematical Programs with Intrinsically Concave Functions

    • U. Passy
    Pages 355-373

  20. Interval Arithmetic in Unidimensional Signomial Programming

    • L. J. Mancini, D. J. Wilde
    Pages 375-387
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Keywords

About this book

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.

Editors and Affiliations

  • Technion-Israel Institute of Technology, Haifa, Israel

    Mordecai Avriel

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