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 The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and

economist An economist is a professional and practitioner in the social sciences, social science discipline of economics. The individual may also study, develop, and apply theories and concepts from economics and write about economic policy. Within this ...

, 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 Stalin Prize may refer to: * The State Stalin Prize in science and engineering and in arts, awarded 1941 to 1954, later known as the USSR State Prize The USSR State Prize (russian: links=no, Государственная премия СССР, ...

in 1949 and the

Nobel Memorial Prize in Economic Sciences 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 ...

in 1975.

Biography

Kantorovich was born on 19 January 1912, to a Russian Jewish family. His father was a doctor practicing in

Saint Petersburg Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...

. In 1926, at the age of fourteen, he began his studies at Leningrad State University. 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 The Government of the Soviet Union ( rus, Прави́тельство СССР, p=prɐˈvʲitʲɪlʲstvə ɛs ɛs ɛs ˈɛr, r=Pravítelstvo SSSR, lang=no), formally the All-Union Government of the Union of Soviet Socialist Republics, commonly ab ...

. He was given the task of

optimizing Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

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 linear programming in 1939, some years before it was advanced by

George Dantzig George Bernard Dantzig (; November 8, 1914 – May 13, 2005) was an American mathematical scientist who made contributions to industrial engineering, operations research, computer science, economics, and statistics. Dantzig is known for his ...

. 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

in 1949. After 1939, he became a professor at

Military Engineering-Technical University The Saint Petersburg Military Engineering-Technical University (Nikolaevsky) (russian: Санкт-Петербургский Военный инженерно-технический университет, VITU), previously known as the Saint Pet ...

. 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 The Road of Life () was the set of ice road transport routes across Lake Ladoga to Leningrad during the Second World War. They were the only Soviet winter surface routes into the city while it was besieged by the German Army Group North under ...

. 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

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 **Ge ...

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 Novosibirsk State University is a public research university located in Novosibirsk, Russia. The university was founded in 1958, on the principles of integration of education and science, early involvement of students with research activities an ...

.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 Tjalling Charles Koopmans (August 28, 1910 – February 26, 1985) was a Dutch-American mathematician and economist. He was the joint winner with Leonid Kantorovich of the 1975 Nobel Memorial Prize in Economic Sciences for his work on the theory ...

, was given "for their contributions to the theory of optimum allocation of resources."

Mathematics

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

, Kantorovich had important results in

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

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 mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators ...

. 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

could be used in the analysis of

iterative method In computational mathematics, an iterative method is a Algorithm, mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the ''n''-th approximation is derived fr ...

s, obtaining the Kantorovich inequalities on the convergence rate 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 Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

, in the theory of the weak convergence of probability measures. Image:Kantorovich (Petrov-Vodkin).jpg, Portrait by Petrov-Vodkin. 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 Pergamon Press was an Oxford-based publishing house, founded by Paul Rosbaud and Robert Maxwell, that published scientific and medical books and journals. Originally called Butterworth-Springer, it is now an imprint of Elsevier. History The cor ...

, 1965. * Klaus Hagendorf (2008)
Spreadsheet presenting all examples of Kantorovich
1939 with the

OpenOffice.org OpenOffice.org (OOo), commonly known as OpenOffice, is a discontinued open-source office suite. Active successor projects include LibreOffice (the most actively developed), Apache OpenOffice, Collabora Online (enterprise ready LibreOffice) a ...

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