Harold W. Kuhn

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Harold William Kuhn (born July 29, 1925 in Santa Monica , California - † July 2, 2014 in New York City , New York ) was an American mathematician who studied game theory .

life and work

Kuhn received his PhD from Princeton University in 1950 with Ralph Fox (Subgroup Theorems for Groups Presented by Generators and Relations). In 1950/51 he was a Fulbright scholar at the University of Paris. From 1951 he taught at Princeton and from 1952 to 1959 at Bryn Mawr College . He was then a professor of mathematics and economics at Princeton. In 1995 he retired. Among other things, he was visiting fellows at the London School of Economics and the University of Rome.

In the 1950s he was a leader in the development of the then still young game theory, where he worked closely with Albert W. Tucker . His friendship with his fellow student John Forbes Nash Jr. , who received the Nobel Prize for Economics during his time at Princeton (also at the instigation of Kuhn) and co-edited Kuhn's works , also dates from this time .

With his teacher Tucker and Gale he gave the first rigorous proof of the duality theorem in linear programming . He became known for the Hungarian method in the assignment problem of combinatorial optimization and operations research and the Karush-Kuhn-Tucker conditions in nonlinear optimization. The Kuhn-Tucker-Karush conditions result from the application of the Lagrange multipliers to the problem of minimizing a (nonlinear) function under constraints formulated by equations and inequalities. A poker version that is simplified for mathematical analysis is named after him.

In 1980 he received the John von Neumann Theory Prize with David Gale and Albert W. Tucker . In 1992 he was elected to the American Academy of Arts and Sciences .

One of his sons is a math professor at the University of Virginia , another is a historian.

Fonts

  • (Ed.): Contributions to the Theory of Games. Volume I (Annals of Mathematical Studies). Princeton University Press, 1950, ISBN 0-691-07934-X , doi : 10.1515 / 9781400881727 .
  • with AW Tucker: Nonlinear Programming. In: Neyman (Ed.): Proceedings of the 2nd Berkeley Symposium 1951. p. 481. (Karush-Kuhn-Tucker conditions)
  • with AW Tucker, D. Gale: Linear Programming and the theory of games. In: Koopmans (Ed.): Activity analysis of allocation and production. 1951.
  • (Ed.): Contributions to the Theory of Games. Volume II (Annals of Mathematical Studies). Princeton University Press, 1953, ISBN 0-691-07935-8 , doi : 10.1515 / 9781400881970 .
  • with G. Szegö (Ed.): Differential Games and related topics. North Holland 1971.
  • The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, Volume 2. 1955, pp. 83-87 (reprinted in Volume 52, 2005, p. 7)
  • with AW Tucker (Ed.): Linear Inequalities and Related Systems. Annals of Mathematical Studies, Princeton University Press, 1956, ISBN 0-691-07999-4 . (therein from Kuhn: On a theorem of Wald .)
  • (Ed.): Classics in Game Theory. Princeton University Press, 1997, ISBN 0-691-01192-3 .
  • (Ed.): The Essential John Nash. Princeton University Press, 2001, ISBN 0-691-09527-2 .
  • Lectures on the Theory of Games. Princeton University Press, 2003, ISBN 0-691-02772-2 .

Web links

Remarks

  1. ^ Harold Kuhn, Princeton mathematician who advanced game theory, dies at 88
  2. ^ Richard Cottle among others George B. Dantzig. In: Notices AMS. March 2007, p. 347. George Dantzig visited Tucker in Princeton in June 1948
  3. ↑ Originally in 1939 in an unpublished diploma thesis by William Karush at the University of Chicago, Fritz John also published similar conditions in 1948 in the Courant Anniversary Volume , but they only became known through the publication of Kuhn and Tucker in 1951. For the history see Richard Cottle, among others, George B Dantzig. In: Notices AMS. March 2007, p. 350
personal data
SURNAME Kuhn, Harold W.
ALTERNATIVE NAMES Kuhn, Harold William
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH July 29, 1925
PLACE OF BIRTH Santa Monica
DATE OF DEATH 2nd July 2014
Place of death New York City