A contextualized historical analysis of the Kuhn-Tucker theorem in nonlinear programming: The impact of World War II

Historia Mathematica

Volumn 27, Issue 4, 2000, Pages 331-361

  Kjeldsen, Tinne Hoff ^a  

^a ROSKILDE UNIVERSITY   (Denmark)

Author keywords

Lagrange multiplier method; Multiple discovery; Nonlinear programming; ONR; Operations research; The calculus of variations; The Kuhn Tucker theorem; The theory of convexity

Indexed keywords

EID: 0034310998     PISSN: 03150860     EISSN: None     Source Type: Journal    
DOI: 10.1006/hmat.2000.2289     Document Type: Article

References (99)

1. Ader O. B. An affine invariant of convex regions. Duke Mathematics Journal. 4:1938;291-299.
2. Albers J. D., Alexanderson G. L. Mathematical People, Profiles and Interviews. 1985.
3. Bazaraa M. S., Sherali H. D., Shetty C. M. Nonlinear Programming, Theory and Algorithms. 1979.
4. Bazaraa M. S., Sherali H. D., Shetty C. M. Nonlinear Programming, Theory and Algorithms. 1993.
5. Behrend F. Über einige Affininvarianten konvexer Bereiche. Mathematische Annalen. 113:1937;713-747.
6. Behrend F. Über die kleinste umbeschriebene und die grosste einbeschriebene Ellipse eines konvexen Bereichs. Mathematische Annalen. 115:1938;379-411.
7. Bellman, R. 1975, Letter to Harold W. Kuhn, dated 11 February, 1975. [Unpublished, copy in possession of the author].
8. Bliss G. A. Normality and abnormality in the calculus of variations. Transactions of the American Mathematical Society. 43:1938;365-376.
9. Brentjes S. Untersuchungen zur Geschichte der linearen Optimierung (LO) von ihren Anfängen bis zur Konstituierung als selbständige mathematische Theorie - Eine Studie zum Problem der Entstehung mathematischer Disziplinen im 20. Jahrhundert. 1975.
10. Brentjes S. Bemerkungen zum Beitrag von Julius Farkas zur Theorie der linearen Optimierung. NTM-Schriftenreihe zur Geschichte der Naturwissenschaften, Technik und Medizin. 13:1976a;21-23.
11. Brentjes S. Der Beitrag der sowjetischen Wissenschaftler zur Entwicklungen der Theorie der linearen Optimierung. NTM-Schriftenreihe zur Geschichte der Naturwissenschaften, Technik und Medizin. 13:1976b;105-110.
12. Browder, F. E.1989. The stone age of mathematics on the midway. In A Century of Mathematics in America, Part II, Peter, Duren, Ed., History of Mathematics, Vol. 2, pp. 191-193. Amer. Math. Soc. Providence, RI.
13. Charnes A., Cooper W. W. On some works of Kantorovich, Koopmans and Others. Management Science. 8:1961;246-263.
14. Cozzens S. E. Social Control and Multiple Discovery in Science: The Opiate Receptor Case. 1989.
15. Dalmedico A. D. L'essor des mathématiques appliquées aux états-Unis: L'impact de la seconde guerre mondiale. Revue d'histoire des mathématiques. 2:1996;149-213.
16. Dantzig G. B. Linear programming. Problems for the Numerical Analysis of the Future. 15:1951;18-21.
17. Dantzig G. B. Linear Programming and Extensions. 1963.
18. Dantzig, G. B.1968. Linear programming and its progeny. In Applications of Mathematical Programming Techniques, E. M. L. Beale, Ed., pp. 3-15. London, English Universities Press.
19. Dantzig G. B. Reminiscences about the origins of linear programming. Operations Research Letters. 1:1982;43-48.
20. Dantzig G. B. Impact of linear programming on computer development. OR/MS Today. 1988;12-17.
21. Dantzig, G. B.1991. Linear Programming. In History of Mathematical Programming, A Collection of Personal Reminiscences, Jan, Karel, Lenstra, Alexander, H. G. Rinnooy Kan, and Alexander, Schrijver, Eds., pp. 19-31. Amsterdam, North-Holland.
22. Dantzig, G. B., and Wood, M. K.1951. The programming of interdependent activities: General discussion. In Activity Analysis of Production and Allocation, Tjalling, C. Koopmans, Ed., Cowles Commission Monographs, Vol. 13, pp. 15-18. New York, Wiley.
23. Dines L. L. Convex extension and linear inequalities. Bulletin of the American Mathematical Society. 42:1936;353-365.
24. Dorfman R. The discovery of linear programming. Annals of the History of Computing. 6:1984;283-295.
25. Dupree A. H. National security and the post-war science establishment in the United States. Nature. 323:1986;213-216.
26. Duren A. L. Graduate student at Chicago in the twenties. The American Mathematical Monthly. 83:1976;243-248.
27. Duren P. History of Mathematics. A century of Mathematics in America, Part II. 2:1989.
28. Farkas G. (J.). Über die Anwendungen des mechanischen Princips von Fourier. Mathematische und Naturwissenschaftliche Berichte aus Ungarn. 12:1895;263-281.
29. Farkas G. (J.). Die algebraischen Grundlagen der Anwendung des Fourier'sschen Principes in der Mechanik. Mathematische und Naturwissenschaftliche Berichte aus Ungarn. 15:1897;25-40.
30. Farkas G. (J.). Die algebraische Grundlage der Anwendungen des mechanischen Princips von Fourier. Mathematische und Naturwissenschaftliche Berichte aus Ungarn. 16:1899;154-157.
31. Farkas G. (J.). Theorie der einfachen Ungleichungen. Journal für die reine und angewandte Mathematik. 124:1901;1-27.
32. Fenchel, W. 1953, Convex Cones, Sets, and Functions, Lecture Notes, Department of Mathematics, Princeton University, 1953.
33. Fortun M., Schweber S. S. Scientists and the legacy of World War II: The case of operations research (OR). Social Studies of Science. 23:1993;595-642.
34. Fourier, J. B. J.1798. Mémoire sur la statique, contenant la démonstration du principe de vitesses virtuelles, et la théorie des momens. In Oeuvres, Gaston, Darboux, Ed., Vol. 2, pp. 475-521. Paris, Gauthier-Villars.
35. Franksen O. I. Irreversibility by inequality constraints. I. On Fourier's inequality. Systems Analysis, Modelling, Simulation. 2:1985a;137-149.
36. Franksen O. I. Irreversibility by inequality constraints. II. The second law of thermodynamics. Systems Analysis, Modelling, Simulation. 3:1985b;251-273.
37. Franksen O. I. Irreversibility by inequality constraints. III. Towards mathematical programming. Systems Analysis, Modelling, Simulation. 4:1985c;337-359.
38. Fraser C. G. Isoperimetric problems in the variational calculus of Euler and Lagrange. Historia Mathematica. 19:1992;4-23.
39. Fraser C. G. The origin of Euler's variational calculus. Archive for History of Exact Sciences. 47:1994;103-141.
40. Gale, D., Kuhn, H. W., and Tucker, A. W.1951. Linear programming and the theory of games. In Activity Analysis of Production and Allocation, Tjalling, C. Koopmans, Ed., Cowles Commission Monographs, Vol. 13, pp. 317-329. New York, Wiley.
41. Gårding, L.1985. Foreword. In Fritz John, Collected Papers, J. Moser, Ed., Vol. 1. Boston, Birkhâuser.
42. Geisler, M. A., and Wood, M. K.1951. Development of dynamic models for program planning. In Activity Analysis of Production and Allocation, Tjalling, C. Koopmans, Ed., Cowles Commission Monographs, Vol. 13, pp. 189-215. New York, Wiley.
43. Grattan-Guinness I. Joseph Fourier's anticipation of linear programming. Operational Research Quaterly. 21:1970;361-364.
44. Grattan-Guinness, I.1994. A new type of question:On the prehistory of linear and non-linear programming, 1770-1940. In The History of Modern Mathematics. III, Eberhard, Knobloch and David, E. Rowe, Eds., pp. 43-89. Boston, Academic Press.
45. Hourshell D. The Cold War, RAND, and the generation of knowledge, 1946-1962. Historical Studies in the Physical and Biological Sciences. 27:1997;237-267.
46. Isbell J. R., Marlow W. H. On an industrial programming problem of Kantorovich. Management Science. 8:1961;13-17.
47. Jessop W. N. Operational research methods: What are they? Operational Research Quaterly. 7:1956;49-58.
48. John F. Moments of inertia of convex regions. Duke Mathematics Journal. 2:1936;447-452.
49. John F. An inequality for convex bodies. University of Kentucky Research Club Bulletin. 8:1942;8-11.
50. John F. Extremum problems with inequalities as subsidiary conditions. Studies and Essays, Presented to R. Courant on his 60th Birthday January 8, 1948. 1948;187-204.
51. Kantorovich, L. V.1939. Mathematical Methods of Organizing and Planning Production. Leningrad, Leningrad University. [In Russian; an English translation can be found in Management Science6, 366-422, 1960.].
52. Kantorovich, L. V.1939. Mathematical Methods of Organizing and Planning Production. Leningrad, Leningrad University. [In Russian; an English translation can be found in Management Science6, 366-422, 1960.].
53. Karush W. Minima of Functions of Several Variables with Inequalities as Side Conditions. 1939.
54. Karush, W. 1975, Letter to Harold W. Kuhn, dated 10 February, 1975. [Unpublished; copy in possession of the author].
55. Kjeldsen T. H. A Contextualised Mathematico-Historical Analysis of Nonlinear Programming: Development and Multiple Discovery. 1999.
56. Koopmans T. C. On the evaluation of Kantorovich's work of 1939. Management Science. 8:1961;264-265.
57. Kuhn H. W. Subgroup theorems for groups presented by generators and relations. Annals of Mathematics. 56:1952;22-46.
58. Kuhn, H. W. 1975a, Letter to William Karush, dated 4 February, 1975. [Unpublished; copy in possession of the author].
59. Kuhn, H. W. 1975b, Letter to William Karush, dated 21 February, 1975. [Unpublished; copy in possession of the author].
60. Kuhn H. W. Nonlinear programming: A historical view. SIAM-AMS Proceedings. 9:1976;1-26.
61. Kuhn H. W. Curriculum Vitae. 1986.
62. Kuhn, H. W, Tucker, A. W. 1995, Some reminiscences, prepared with the assistance of Alan and Tom Tucker. Based on an oration given by Harold W. Kuhn, Notices of the AMS, October 1995.
63. Kuhn, H. W. 1998, Personal interview, Princeton University, Princeton, NJ, 23 April, 1998.
64. Kuhn, H. W., and Tucker, A. W.1950. Nonlinear programming, In Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, J. Neyman, Ed., pp. 481-492. Berkeley.
65. Lagrange, J. L.1788. Méchanique analitique, 1788. Reprint ed., 1965, Paris, Albert Blanchard.
66. Leifman L. J. Functional Analysis, Optimization, and Mathematical Economics: A Collection of Papers Dedicated to the Memory of Leonid Vital'evich Kantorovich. 1990.
67. Leonard, R. J.1992. Creating a context for game theory. In Towards a History of Game Theory, E. Roy, Weintraub, Ed., pp. 29-76. Durham/London, Duke University Press.
68. Leonard R. J. From parlor games to social science: Von Neumann, Morgenstern, and the creation of game theory 1928-1944. Journal of Economic Literature. 33:1995;730-761.
69. Luenberger D. G. Linear and Nonlinear Programming. 1973.
70. MacLane, S.1989. Mathematics at the University of Chicago, A brief history. In A Century of Mathematics in America, part II, Peter, Duren, Ed., American Mathematical Society, History of Mathematics, Vol. 2, pp. 127-154. Providence, RI, Amer. Math. Soc.
71. Merton, R. K.1973. Singletons and multiples in science. In The Sociology of Science, Theoretical and Empirical Investigations, Robert, K. Merton, Ed., pp. 343-382. Chicago, Univ. of Chicago Press.
72. Mirowski, P.1991. When games grow deadly serious: The military influence on the evolution of game theory. In Economics and National Security, D. G. Goodwin, Ed., Annual Supplement to History of Political Economy, Vol. 23, pp. 227-255. Durham/London, Duke Univ. Press.
73. Morse P. M. Where is the new blood? Journal of the Operations Research Society of America. 3:1955;383-387.
74. Morse P. M. Training in operations research at the Massachusetts Institute of Technology. Operations Research. 4:1956;733-735.
75. Moser J. Fritz John, Collected Papers. 1:1985.
76. Old B. S. The evolution of the Office of Naval Research. Physics Today. 14:1961;30-35.
77. Ostrogradsky M. V. Considérations générales sur les momens des forces. Mémoires de l'Académie impériale des sciences de St.-Pétersbourg, Sixième Série. 1:1838;129-150.
78. Parshall K. H., Rowe D. E. History of Mathematics. The Emergence of the American Mathematical Research Community, 1876-1900: J. J. Sylvester, Felix Klein, and E. H. Moore. 8:1994.
79. Patinkin D. Multiple discoveries and the central message. American Journal of Sociology. 89:1983;306-323.
80. Peressini A. L., Sullivan F. E., Uhl J. J. The Mathematics of Nonlinear Programming. 1988.
81. Prager W. Introductory Remarks. Quarterly of Applied Mathematics. 30:1972;1-9.
82. Prékopa A. On the development of optimization theory. American Mathematical Monthly. 87:1980;527-542.
83. Rau, E.The adoption of operations research in the United States during World War II. In Systems, Experts, and Computers, A. C. Hughes and Tom, P. Hughes, Eds., Dibner Series, Jed, Z. Buchwald, Ed., Cambridge, MA, MIT Press (to appear).
84. Rees M. S. The mathematics program of the Office of Naval Research. Bulletin of the American Mathematical Society. 1948;1-5.
85. Rees, M. S.1977a. Mathematics and the government: The post-war years as augury of the future. In The Bicentennial Tribute to American Mathematics, 1776-1976, D. Tarwater, Ed., pp. 101-116. Buffalo, NY, The Mathematical Association of America.
86. Rees M. S. Early years of the mathematics program at ONR. Naval Research Reviews. 30:1977b;22-29.
87. Reid C. Courant in Göttingen and New York. The Story of an Improbable Mathematician. 1976.
88. Roy R. H. Operations research at the Johns Hopkins University. Operations Research. 4:1956;735-738.
89. Sapolsky, H. M.1979. Academic science and the military: The years since the Second World War. In The Sciences in the American Context: New Perspectives, Reingold, Ed., pp. 379-399. Washington, D.C. Smithsonian Institution Press.
90. Schweber, S. S.1988. The mutual embrace of science and the military: ONR and the growth of physics in the United States after World War II. In Science, Technology and the Military, E. Mendelsohn, M. R. Smith, and P. Weingart, Eds., pp. 3-45. Dordrecht, Kluwer Academic.
91. Smith B. The RAND Corporation, Case Study of a Nonprofit Advisory Corporation. 1969.
92. Stokes R. W. A geometric theory of linear inequalities. Transactions of the American Mathematical Society. 33:1931;782-805.
93. Stone, M. H.1989. Reminiscences of mathematics at Chicago. In A Century of Mathematics in America, Part II, Peter Duren, Ed., History of Mathematics, Vol. 2, pp. 183-190. Providence, RI, Amer. Math. Soc.
94. Takyama A. Mathematical Economics. 1974.
95. Tucker A. W. Curriculum Vitae. 1980.
96. Ulam S. John von Neumann. Bulletin of the American Mathematical Society. 64:1958;1903-1957.
97. von Neumann, J.1947. Discussion of a maximum problem. In John von Neumann Collected Works, A. H. Taub, Ed., Vol. 6, pp. 89-95. Taub, Oxford, Pergamon.
98. von Neumann, J, and, Morgenstern, O. Theory of Games and Economic Behavior, Princeton, NJ, Princeton Univ. Press.
99. Zachary P. G. Endless Frontier: Vannevar Bush, Engineer of the American Century. 1997.