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Leonid Vitaliyevich Kantorovich (Russian: Леони́д Вита́льевич Канторо́вич) (19 January 1912, Saint Petersburg – 7 April 1986, Moscow) was a Soviet/Russian 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).

During the Siege of Leningrad, Kantorovich was 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."


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 of mass transfer. His analysis proposed the Kantorovich metric, which is used in probability theory, in the theory of the weak convergence of probability measures.

See also

* List of economists


* 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 Calc Solver as well as the lp_solver.

External links

* Leonid Kantorovich (with a small photo)
* contributions to the theory of optimum allocation of resources.
* koopmans lecture - pdf
* O'Connor, John J.; Robertson, Edmund F., "Leonid Kantorovich", MacTutor History of Mathematics archive, University of St Andrews, . (With additional photos.)
* Leonid Kantorovich at the Mathematics Genealogy Project
* (Russian)Biography on the homepage of Sobolev Institute of Mathematics, in Russian
* (Russian) On Leonid Kantorovich and linear programming (in Russian), by Anatoly Vershik
* The World Line of Kantorovich - by S.S. Kutateladze
* Kantorovich's Phenomenon - by S.S. Kutateladze


Mathematics Encyclopedia

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