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Leonid Kantorovich

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Leonid Kantorovich
Leonid Kantorovich in 1975
Born(1912-01-19)19 January 1912
Saint Petersburg, Russian Empire
Died7 April 1986(1986-04-07) (aged 74)
Moscow, Russia, USSR
NationalitySoviet
Alma materLeningrad State University
Known forLinear programming
Kantorovich theorem
normed vector lattice (Kantorovich space)
Kantorovich metric
Kantorovich inequality
approximation theory
iterative methods
functional analysis
numerical analysis
scientific computing
AwardsSveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (1975)
Scientific career
FieldsMathematics

Leonid Vitaliyevich Kantorovich (Russian: Леони́д Вита́льевич Канторо́вич) (19 January 1912, Saint Petersburg – 7 April 1986, Moscow) was a Soviet mathematician and economist, known for his theory and development of techniques for the optimal allocation of resources. He was the winner of the Nobel Prize in Economics in 1975 and the only winner of this prize from the USSR.

Kantorovich worked for the Soviet government. He was given the task of optimizing production in a plywood industry. He came up (1939) with the mathematical technique now known as linear programming, some years before it was reinvented and much advanced by George Dantzig. He authored several books including The Mathematical Method of Production Planning and Organization and The Best Uses of Economic Resources. For his work, Kantorovich was awarded Stalin Prize (1949).

After 1939, he becomes the professor of Military engineering-technical university (Russian: Военный инженерно-технический университет). During the Siege of Leningrad, Kantorovich was the professor of VITU of Navy and in charge of safety on the Road of Life. He calculated the optimal distance between cars on ice, depending on thickness of ice and temperature of the air. In December 1941 and January 1942, Kantorovich personally walked between cars driving on the ice of Lake Ladoga, on the Road of Life, to ensure the cars did not sink. However, many cars with food for survivors of the siege were destroyed by the German air-bombings.

For his feat and courage Kantorovich was awarded the Order of the Patriotic War, and was decorated with the medal For Defense of Leningrad.

The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, which he shared with Tjalling Koopmans, was given "for their contributions to the theory of optimal allocation of resources."

  • Portrait by Petrov-Vodkin. 1938.
    Portrait by Petrov-Vodkin. 1938.
  • 1976
    1976
  • Original CIA file on Kantorovich, seized from the former US Embassy in Tehran.
    Original CIA file on Kantorovich, seized from the former US Embassy in Tehran.

Mathematics

In mathematical analysis, Kantorovich had important results in functional analysis, approximation theory, and operator theory.

In particular, Kantorovich formulated fundamental results in the theory of normed vector lattices, which are called "K-spaces" in his honor.

Kantorovich showed that functional analysis could be used in the analysis of iterative methods, obtaining the Kantorovich inequalities on the convergence rate of the gradient method and of Newton's method.

Kantorovich considered infinite-dimensional optimization problems, such as the Kantorovich-Monge problem in transportation theory. His analysis proposed the Kantorovich metric, which is used in probability theory, in the theory of the weak convergence of probability measures.

See also

References

Nobel prize lecture

Further reading

  • Dantzig, George, Linear programming and extensions. Princeton University Press and the RAND Corporation, 1963. Cf. p.22 for the work of Kantorovich.
  • Isbell, J.R.; Marlow, W.H., "On an Industrial Programming Problem of Kantorovich", Management Science, Vol. 8, No. 1 (Oct., 1961), pp. 13–17
  • Koopmans, Tjalling C., "Concepts of optimality and their uses", Nobel Memorial Lecture, December 11, 1975
  • Kutateladze, S.S., "The World Line of Kantorovich", Notices of the ISMS, International Society for Mathematical Sciences, Osaka, Japan, January 2007
  • Kutateladze, S.S., "Kantorovich's Phenomenon", Siberian Math. J. (Сибирский мат. журн.), 2007, V. 48, No. 1, 3–4, November 29, 2006.
  • Kutateladze, S.S., "Mathematics and Economics of Kantorovich"
  • Leifman, Lev J., ed. (1990). Functional analysis, optimization, and mathematical economics: A collection of papers dedicated to the memory of Leonid Vitalʹevich Kantorovich. New York: The Clarendon Press, Oxford University Press. pp. xvi+341. ISBN 0-19-505729-5. MR1082562. {{cite book}}: Cite has empty unknown parameter: |1= (help)CS1 maint: multiple names: authors list (link)
    • Makarov, V. L. [Valeriĭ Leonidovich]; Sobolev, S. L. "Academician L. V. Kantorovich (19 January 1912 to 7 April 1986)". pp. 1–7. MR1082564. {{cite book}}: Cite has empty unknown parameters: |1= and |2= (help); Missing or empty |title= (help)
    • Kantorovich, L. V. "My journey in science (supposed report to the Moscow Mathematical Society)" [expanding Russian Math. Surveys 42 (1987), no. 2, pp. 233–270]. pp. 8–45. MR898626. {{cite book}}: Cite has empty unknown parameters: |1= and |2= (help)
  • Template:Cite article
  • Template:Ru icon Vershik, Anatoly, et al., "Leonid V. Kantorovich (1912-1986)", Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. Also published in the Siberian Mathematical Journal, Volume 43 (2002), No. 1, pp. 3–8
  • Template:Ru icon Vershik, Anatoly, "On Leonid Kantorovich and linear programming"

External links

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