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Birkhäuser

Traces and Emergence of Nonlinear Programming

  • Book
  • © 2014

Overview

Editors:
  1. Giorgio Giorgi

    1. Sez. Matematica Generale, Universita Pavia Dipto. Ricerche Aziendali, Pavia, Italy

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  2. Tinne Hoff Kjeldsen

    1. IMFUFA, NSM, Roskilde University, Roskilde, Denmark

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    You can also search for this editor in PubMed   Google Scholar

  • The book offers for the first time a collection of the basic historical papers on nonlinear programming

  • The book includes a full version of the famous Master Thesis of William Karush (1939), where the main theorem of nonlinear programming appeared for the first time

  • The book provides a useful history of mathematical programming?

  • Includes supplementary material: sn.pub/extras

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. A Historical View of Nonlinear Programming: Traces and Emergence

    • Giorgio Giorgi, Tinne Hoff Kjeldsen
    Pages 1-43

  3. A Gradient Method For Approximating Saddle Points and Constrained Maxima

    • Kenneth J. Arrow, Leonid Hurwicz
    Pages 45-60

  4. Reduction of Constrained Maxima to Saddle-Point Problems

    • Kenneth J. Arrow, Leonid Hurwicz
    Pages 61-80

  5. Constraint Qualifications in Maximization Problems

    • Kenneth J. Arrow, Leonid Hurwicz, Hirofumi Uzawa
    Pages 81-97

  6. Normality and Abnormality in the Calculus of Variations

    • Gilbert A. Bliss
    Pages 99-110

  7. A Theorem of Fritz John in Mathematical Programming

    • Richard W. Cottle
    Pages 111-123

  8. On Conjugate Convex Functions

    • Werner Fenchel
    Pages 125-129

  9. Programming in Linear Spaces

    • Leonid Hurwicz
    Pages 131-195

  10. Extremum Problems with Inequalities as Subsidiary Conditions

    • Fritz John
    Pages 197-215

  11. Minima of Functions of Several Variables with Inequalities as Side Conditions

    • William Karush
    Pages 217-245

  12. Nonlinear Programming

    • Harold W. Kuhn, Albert W. Tucker
    Pages 247-258

  13. Second Order Conditions for Constrained Minima

    • Garth P. McCormick
    Pages 259-270

  14. An Indirect Sufficiency Proof for the Problem of Lagrange with Differential Inequalities as Added Side Conditions

    • Louis L. Pennisi
    Pages 271-292

  15. Lagrange Multipliers Revisited

    • Morton Slater
    Pages 293-306

  16. The Kuhn-Tucker Theorem in Concave Programming

    • Hirofumi Uzawa
    Pages 307-312

  17. The Problem of Lagrange with Differential Inequalities as Added Side Conditions

    • Frederick Albert Valentine
    Pages 313-357

  18. On Linear Inequalities

    • Lloyd L. Dines, N. H. McCoy
    Pages 359-392

  19. Nonlinear Programming: A Historical View

    • Harold W. Kuhn
    Pages 393-414

  20. Recherches Sur La Méthode de Maximis et Minimis.

    • Miscellanea Taurinensia
    Pages 415-434
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Keywords

About this book

The book contains reproductions of the most important papers that gave birth to the first developments in nonlinear programming. Of particular interest is W. Karush's  often quoted Master Thesis, which is published for the first time. The anthology includes an extensive preliminary chapter, where the editors trace out the history of mathematical programming, with special reference to linear and nonlinear programming.​

Reviews

From the book reviews:

“The present volume has collected the classical papers that laid down the foundations of nonlinear optimizations. … The book is invaluable for those who would like to see the origin of nonlinear programming. It is very helpful for teachers and students of the field.” (Péter Hajnal, Acta Scientiarum Mathematicarum (Szeged), Vol. 80 (1-2), 2014)

Editors and Affiliations

  • Sez. Matematica Generale, Universita Pavia Dipto. Ricerche Aziendali, Pavia, Italy

    Giorgio Giorgi

  • IMFUFA, NSM, Roskilde University, Roskilde, Denmark

    Tinne Hoff Kjeldsen

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