William Karush

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William Karush (born March 1, 1917 in Chicago , † February 22, 1997 ) was an American mathematician.

Karush studied mathematics at the University of Chicago with a master’s degree in 1939 and a doctorate in 1942 under Magnus Hestenes ( Isoperimetric problems and Index theorems in the Calculus of Variations ). During World War II he worked on the Manhattan Project in Chicago and Oak Ridge (Tennessee) . He was one of 70 scientists who signed the Szilard petition against the use of the atomic bomb. From 1945 he was an instructor and then an associate professor at the University of Chicago, before he went into industry in 1956 (first to the Ramo-Wooldridge Corporation, from 1958 to the System Development Corporation ) and worked in operations research . From 1967 until his retirement in 1987 he was a mathematics professor at California State University in Northridge. He died in California from complications from an operation.

He dealt with mathematical optimization , operations research, calculus of variations and dynamic optimization . Karush and his wife Rebecca were close friends of the father of dynamic optimization, Richard Bellman .

In 1939 he introduced the Karush-Kuhn-Tucker conditions in his master’s thesis ( Minima of Functions of Several Variables with Inequalities as Side Constraints ) at Lawrence M. Graves , but this was only possible after a conference publication by Harold W. Kuhn and Albert W. Tucker became known and are also named after them. Karush had not published his results and they were rediscovered independently by Kuhn and Tucker. For a long time it was only called Kuhn-Tucker's sentence, until the previous role of Karush was revealed (with Kuhn himself being involved in several publications on the story). Karush's master's thesis also includes the Fritz-John conditions . Karush later gave as a reason for not publishing his result that it was then only a by-product of the Chicago seminar on calculus of variations that was still in existence at the time (an intermediate step on his way to Ph. D.) and the later applications in mathematics Optimization not yet apparent.

He published two mathematics lexicons and dictionaries.

He was married and had a son and a daughter.

literature

  • TH Kjeldsen, A contextualized historical analysis of the Kuhn – Tucker Theorem in nonlinear programming: The impact of World War II, Historia Mathematica, Volume 27, 2000, pp. 331–361
  • Richard Cottle, William Karush and the KKT Theorem, Documenta Mathematica, Extra Volume ISMP, 2012, 255-269, pdf

Individual evidence

  1. ↑ William Karush in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ Between 1949 and 1952 he worked in numerical analysis for the National Bureau of Standards in Los Angeles ( UCLA ) and in 1953 for Hughes Aircraft. 1955/56 he was a Ford Faculty Fellow at UCLA.
  3. ^ Kuhn, Nonlinear programming: A historical view, in RW Cottle, CE Lemke (Ed.), Nonlinear Programming, SIAM-AMS Proceedings, Vol. 9, American Mathematical Society, Providence, 1976
  4. ↑ Kuhn only found out about Karush's work in 1974 from the book by Takayama Mathematical Economics (Dryden Press 1974). Independently around the same time, Magnus Hestenes had remembered the work and urged Karush to go public, as Karush wrote in a correspondence with Kuhn. There were references to Karush as early as 1953 in the literature (Louis Pennisi, Trans. AMS, 74, 177-198) and in works by MA El-Hodiri in the 1960s (about whom Takayama found out about it).
  5. ^ The crescent dictionary of mathematics, Macmillan 1962
  6. ^ Webster's new world dictionary of mathematics, 1989
personal data
SURNAME Karush, William
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH March 1, 1917
PLACE OF BIRTH Chicago
DATE OF DEATH February 22, 1997