Leonid Kantorovich

Leonid Kantorovich
Leonid Kantorovich in 1975
Born	(1912-01-19)19 January 1912 Saint Petersburg, Russian Empire
Died	Moscow, Russia, USSR
Nationality	Soviet
Fields	Mathematics
Alma mater	Leningrad State University
Doctoral advisor	Grigorii Fichtenholz Vladimir Smirnov
Known for	Linear programming Kantorovich theorem normed vector lattice (Kantorovich space) Kantorovich metric Kantorovich inequality approximation theory iterative methods functional analysis numerical analysis scientific computing
Notable awards	Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (1975)

Leonid Vitaliyevich Kantorovich (Russian: Леони́д Вита́льевич Канторо́вич; IPA: [lʲɪɐˈnʲit vʲɪˈtalʲɪvʲɪtɕ kəntɐˈrovʲɪtɕ]) (19 January 1912 – 7 April 1986) was a Soviet mathematician and economist, known for his theory and development of techniques for the optimal allocation of resources. He is regarded as the founder of linear programming. He was the winner of the Stalin Prize in 1949 and the Nobel Prize in Economics in 1975.

Biography

Kantorovich was born on 19 January 1912, to a Russian Jewish family. His father was a doctor practicing in Saint Petersburg. In 1926, at the age of fourteen, he began his studies at the Leningrad University. He graduated from the Faculty of Mathematics in 1930, and began his graduate studies. In 1934, at the age of 22 years, he became a full professor.

Later, 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 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 the Stalin Prize in 1949.

After 1939, he became the professor of Military engineering-technical university. 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.

Since 1960, Kantorovich lived and worked in Novosibirsk, where he created and took charge of the Department of Calculus Mathematics in Novosibirsk State University.

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 optimum allocation of resources."

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 (see the Kantorovich theorem).

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.

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  Portrait by Petrov-Vodkin. 1938.

• Leonid Kantorovich 1976.jpg

  1976

• Espionage den04 40.png

  Original CIA file on Kantorovich, seized from the former US Embassy in Tehran.

See also

• List of economists
• List of Russian mathematicians

References

• V. Makarov (1987). "Kantorovich, Leonid Vitaliyevich" The New Palgrave: A Dictionary of Economics, v. 3, pp. 14–15.
• L.V. Kantorovich (1939). "Mathematical Methods of Organizing and Planning Production" Management Science, Vol. 6, No. 4 (Jul., 1960), pp. 366–422.
• Klaus Hagendorf (2008). Spreadsheet presenting all examples of Kantorovich, 1939 with the OpenOffice.org Calc Solver as well as the lp_solver.

Nobel prize lecture

• Kantorovich, Leonid, "Mathematics in Economics: Achievements, Difficulties, Perspectives", Nobel Prize lecture, December 11, 1975
• "Autobiography: Leonid Kantorovich", Nobel Prize website

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"
• (Russian) Vershik, Anatoly, et al., "Leonid V. Kantorovich (1912–1986)", Sobolev Institute of Mathematics of the Siberian Division of the Russian Academy of Sciences. Also published in the Siberian Mathematical Journal, Volume 43 (2002), No. 1, pp. 3–8
• (Russian) Vershik, Anatoly, "On Leonid Kantorovich and linear programming"

External links

• . (With additional photos.)
• Leonid Kantorovich at the Mathematics Genealogy Project
• Information about: Leonid Vitaliyevich Kantorovich – IDEAS/RePEc

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