Harold W. Kuhn

Harold William Kuhn ( born July 29, 1925 in Santa Monica ) is an American mathematician who dealt with game theory.

Kuhn received his doctorate in 1950 from Princeton University with Ralph Fox ( subgroup theorem for Groups Presented by generator and relations). 1950/51 he was a Fulbright Fellow at the University of Paris. From 1951 he taught at Princeton and 1952-1959 at Bryn Mawr College. After that, he was Professor of Mathematics and Economics at Princeton. In 1995 he became Professor Emeritus. He also served as a guest stays at the London School of Economics and the University of Rome.

He was in the 1950s, leading the development of the then fledgling game theory, where he worked closely with Albert W. Tucker. From this period dates his friendship with his fellow student John Forbes Nash Jr., who ( at the instigation of Kuhn ) was awarded the Nobel Prize in Economics for work in game theory in his time at Princeton and whose works are published by Kuhn.

With his teacher Tucker and Gale, he gave the first rigorous proof of the Dualitätstheorems in the linear programming He is known for the Hungarian method for the allocation problem ( Assignment problem) combinatorial optimization and operations research and the Karush -Kuhn - Tucker conditions in nonlinear optimization. The Kuhn- Tucker - Karush conditions are obtained as an application of Lagrange multipliers to the problem of a (nonlinear ) function under formulated by equations and inequalities constraints to minimize. A simplified mathematical analysis for the poker version is named after him.

In 1980 he was awarded the John von Neumann Theory Prize with David Gale ( economist ) and Albert W. Tucker.

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

Writings

  • (Ed.): Contributions to the Theory of Games. Part 1 Princeton University Press, 1950, ISBN 0 - 691-07934 -X. ( Annals of Mathematical Studies. )
  • With A. W. Tucker: Nonlinear Programming. In: Neyman (ed.). Proceedings of the 2nd Berkeley Symposium, 1951 p 481 ( Karush -Kuhn - Tucker conditions )
  • AW Tucker, D. Gale: Linear Programming and the theory of games. In: Koopmans (ed.) Activity analysis of production and allocation. In 1951.
  • (Ed.): Contributions to the Theory of Games. Part 2 Princeton University Press, 1953, ISBN 0-691-07935-8. ( Annals of Mathematical Studies. )
  • With G. Szego (eds.): Differential games and related topics. North Holland 1971.
  • The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, Vol 2 1955, pp. 83-87 ( in Volume 52, 2005, p 7 reprinted )
  • AW Tucker ( eds.): Linear Inequalities and Related Systems. Annals of Mathematical Studies, Princeton University Press, 1956, ISBN 0-691-07999-4. ( in Kuhn: On a theorem of forest. )
  • (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.
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