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William Karush role in the karush-kuhn-tucker theorem | ||
| نشریه ریاضی و جامعه | ||
| Article 5, Volume 1, Issue 2, June 2016, Pages 67-75 PDF (1.5 M) | ||
| Document Type: Research Paper | ||
| DOI: 10.22108/msci.2016.6789 | ||
| Author | ||
| Shahnaz Esmaeili* | ||
| Department of Mathematics, University of Isfahan | ||
| Abstract | ||
| This paper is mainly about William Karush and his role in the Karush-Kuhn-Tucker theorem of nonlinear programming. It tells the story of fundamental optimization results that William Karush obtained in his masters thesis. The principal resultwhich concerns necessary conditions of optimality for minimize a function of several variables constrained by inequalitiesfirst became known as the KuhnTucker theorem that Harold Kuhn and Albert Tucker it proved in 1950. It was while that in 1939 William Karush this theorem had been proven already in his masters thesis, which was unpublished. In the meantime, what was led to surprises all this was that William Karush neither only did not published them but even not advertised. This results years later, were independently rediscovered and published by Kuhn and Tucker. | ||
| Keywords | ||
| Karush-Kuhn-Tucker theorem; Non-linear programming | ||
| References | ||
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[1] R. Bellman, Letter to Harold W. Kuhn, dated 11 February, 1975, [Unpublished, copy in possession of the author.] [2] G. A. Bliss, G. A. 1938, Normality and abnormality in the calculus of variations, Trans. Amer. Math. Soc., 43 (1938) 365–376. [3] R. W. Cottle, William Karush and the KKT Theorem, Documenta Math., Extra Volume ISMP, 2012 255-265. [4] W. Karush, Minima of Functions of Several Variables with Inequalities as Side Conditions, Department of Mathematics, University of Chicago, 1939. [5] W. Karush, Letter to Harold W. Kuhn, dated 10 February, 1975, [Unpublished; copy in possession of the author.] [6] W. Karush, The Crescent Dictionary of Mathematics, The Macmillan Company, New York, 1962. [7] W. Karush, Webster’s New World Dictionary of Mathematics, MacMillan, New York, 1989. [8] T. H. Kjeldson, A Contextualized Historical Analysis of the Kuhn–Tucker Theorem in Nonlinear Programming: The Impact of World War II, Historia Mathematica, 27 (2000) 331–361. [9] H. W. Kuhn, Nonlinear programming: A historical view, SIAM–AMS Proceedings, 9 (1976) 1–26. [10] H. W. Kuhn, Letter to William Karush, dated 4 February, 1975, [Unpublished; copy in possession of the author.] [11] K. H. Parshall and D. E. Rowe, The Emergence of the American Mathematical Research Community, 1876–1900: J. J. Sylvester, Felix Klein, and E. H. Moore, History of Mathematics, Providence, Amer. Math. Soc., 8 1994. [12] A. Takayama, A. Mathematical Economics, Hinsdale, IL: Dryden, 1974. | ||
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