Leonid Vitalyevich Kantorovich ( rus, Леони́д Вита́льевич Канторо́вич, , p=lʲɪɐˈnʲit vʲɪˈtalʲjɪvʲɪtɕ kəntɐˈrovʲɪtɕ, a=Ru-Leonid_Vitaliyevich_Kantorovich.ogg; 19 January 19127 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 Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear function#As a polynomial function, li ...

. He was the winner of the Stalin Prize in 1949 and the Nobel Memorial Prize in Economic Sciences in 1975.

Biography

Kantorovich was born on 19 January 1912, to a

Russian Jewish The history of the Jews in Russia and areas historically connected with it goes back at least 1,500 years. Jews in Russia have historically constituted a large religious and ethnic diaspora; the Russian Empire at one time hosted the largest pop ...

family. His father was a doctor practicing in Saint Petersburg. In 1926, at the age of fourteen, he began his studies at

Leningrad State University Saint Petersburg State University (SPBU; russian: Санкт-Петербургский государственный университет) is a public research university in Saint Petersburg, Russia. Founded in 1724 by a decree of Peter the G ...

. He graduated from the Faculty of Mathematics and Mechanics 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 Plywood is a material manufactured from thin layers or "plies" of wood veneer that are glued together with adjacent layers having their wood grain rotated up to 90 degrees to one another. It is an engineered wood from the family of manufactured ...

industry. He devised the mathematical technique now known as

in 1939, some years before it was advanced by George Dantzig. He authored several books including ''The Mathematical Method of Production Planning and Organization'' (Russian original 1939), ''The Best Uses of Economic Resources'' (Russian original 1959), and, with Vladimir Ivanovich Krylov, ''Approximate methods of higher analysis'' (Russian original 1936). For his work, Kantorovich was awarded the Stalin Prize in 1949. After 1939, he became a professor at Military Engineering-Technical University. During the

Siege of Leningrad The siege of Leningrad (russian: links=no, translit=Blokada Leningrada, Блокада Ленинграда; german: links=no, Leningrader Blockade; ) was a prolonged military blockade undertaken by the Axis powers against the Soviet city of L ...

, Kantorovich was a professor at VITU of Navy and worked on safety of the Road of Life. He calculated the optimal distance between cars on ice in dependence of the thickness of ice and the temperature of the air. In December 1941 and January 1942, Kantorovich walked himself between cars driving on the ice of Lake Ladoga on the Road of Life to ensure that cars did not sink. However, many cars with food for survivors of the siege were destroyed by the

German German(s) may refer to: * Germany (of or related to) **Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ger ...

airstrikes. In 1948 Kantorovich was assigned to the atomic project of the USSR. For his feat and courage Kantorovich was awarded the

Order of the Patriotic War The Order of the Patriotic War (russian: Орден Отечественной войны, Orden Otechestvennoy voiny) is a Soviet military decoration that was awarded to all soldiers in the Soviet armed forces, security troops, and to partisan ...

, and was decorated with the medal ''For Defense of Leningrad''. After 1960, Kantorovich lived and worked in

Novosibirsk Novosibirsk (, also ; rus, Новосиби́рск, p=nəvəsʲɪˈbʲirsk, a=ru-Новосибирск.ogg) is the largest city and administrative centre of Novosibirsk Oblast and Siberian Federal District in Russia. As of the Russian Census ...

, where he created and took charge of the Department of Computational Mathematics in Novosibirsk State University.Kantorovich`s biography in Russian
/ref> The

Nobel Memorial Prize The Nobel Memorial Prize in Economic Sciences, officially the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel ( sv, Sveriges riksbanks pris i ekonomisk vetenskap till Alfred Nobels minne), is an economics award administered ...

, 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 In mathematics, approximation theory is concerned with how function (mathematics), functions can best be approximation, approximated with simpler functions, and with quantitative property, quantitatively characterization (mathematics), characteri ...

, and operator theory. In particular, Kantorovich formulated some fundamental results in the theory of normed vector lattices, especially in Dedekind complete vector lattices called "K-spaces" which are now referred to as "Kantorovich 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 In numerical analysis, the order of convergence and the rate of convergence of a convergent sequence are quantities that represent how quickly the sequence approaches its limit. A sequence (x_n) that converges to x^* is said to have ''order of co ...

of the

gradient method In optimization (mathematics), optimization, a gradient method is an algorithm to solve problems of the form :\min_\; f(x) with the search directions defined by the gradient of the function at the current point. Examples of gradient methods are t ...

and of

Newton's method In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valu ...

(see the

Kantorovich theorem The Kantorovich theorem, or Newton–Kantorovich theorem, is a mathematical statement on the semi-local convergence of Newton's method. It was first stated by Leonid Kantorovich in 1948. It is similar to the form of the Banach fixed-point theorem, ...

). Kantorovich considered

infinite-dimensional optimization In certain optimization problems the unknown optimal solution might not be a number or a vector, but rather a continuous quantity, for example a function or the shape of a body. Such a problem is an infinite-dimensional optimization problem, becaus ...

problems, such as the Kantorovich-Monge problem in transport theory. His analysis proposed the Kantorovich-Rubinstein metric, which is used in probability theory, in the theory of the weak convergence of

probability measure In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space that satisfies measure properties such as ''countable additivity''. The difference between a probability measure and the more gener ...

s. Image:Kantorovich (Petrov-Vodkin).jpg, Portrait by

Petrov-Vodkin Kuzma Sergeevich Petrov-Vodkin, (; November 5, Old_Style_and_New_Style_dates.html" ;"title="nowiki/> O. S. 24 October1878 – February 15, 1939) was a Russian and USSR">Soviet painter. His early iconographic work used special creative effe ...

. 1938. Image:Leonid Kantorovich 1976.jpg, 1976 File:Espionage den04 40.png, Original CIA file on Kantorovich, seized from the former US Embassy in Tehran.

Notes

References

* * * Kantorovich, L.V. (1959).
"The Best Use of Economic Resources"
'(). Pergamon Press, 1965. * 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

Nobel Prize website

External links

* * (With additional photos.)

– IDEAS/RePEc *
Biography Leonid Kantorovich
from the Institute for Operations Research and the Management Sciences
Biographical documentary about L.Kantorovich
by '' Rossiya-Culture''

* {{DEFAULTSORT:Kantorovich, Leonid 1912 births 1986 deaths 20th-century Russian economists 20th-century Russian mathematicians Mathematicians from Saint Petersburg People from Sankt-Peterburgsky Uyezd Fellows of the Econometric Society Full Members of the USSR Academy of Sciences Military Engineering-Technical University faculty Novosibirsk State University academic personnel Saint Petersburg State University alumni Saint Petersburg State University faculty Nobel laureates in Economics Stalin Prize winners Lenin Prize winners Recipients of the Order of Lenin Recipients of the Order of the Red Banner of Labour Approximation theorists Functional analysts General equilibrium theorists Mathematical economists Operations researchers Operator theorists Variational analysts Russian economists Russian Jews Russian mathematicians Soviet economists Soviet Jews Soviet mathematicians Soviet Nobel laureates Burials at Novodevichy Cemetery

Biography

Mathematics

See also

Notes

References

Further reading

External links