Traces and Emergence of Nonlinear Programming

1. Front Matter

   Pages i-xvi

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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

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.​

• Duality theory
• History of mathematical programming
• History of nonlinear programming
• Nonlinear programming
• Optimality conditions in nonlinear programming

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)

• 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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