Leonid Vitalyevich Kantorovich (, ; 19 January 19127 April 1986) was a Soviet

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, mathematical structure, structure, space, Mathematica ...

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 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 and objective are represented by linear function#As a polynomia ...

. He was the winner of the Stalin Prize 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 (), commonly referred to as the Nobel Prize in Economics(), is an award in the field of economic sciences adminis ...

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, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland ...

. 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. In 1935 he received his doctoral degree. Later, Kantorovich worked for the

Soviet government The Government of the Union of Soviet Socialist Republics (USSR) was the executive and administrative organ of the highest body of state authority, the All-Union Supreme Soviet. It was formed on 30 December 1922 and abolished on 26 December 199 ...

. He was given the task of optimizing production in a plywood 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 was a Siege, military blockade undertaken by the Axis powers against the city of Leningrad (present-day Saint Petersburg) in the Soviet Union on the Eastern Front (World War II), Eastern Front of World War II from 1941 t ...

, 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 Lake Ladoga is a freshwater lake located in the Republic of Karelia and Leningrad Oblast in northwestern Russia, in the vicinity of Saint Petersburg. It is the largest lake located entirely in Europe, the second largest lake in Russia after Lake ...

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 airstrikes. For his feat and courage Kantorovich was awarded the Order of the Patriotic War, and was decorated with the medal ''For Defense of Leningrad''. In 1948 Kantorovich was assigned to the atomic project of the USSR. After 1960, Kantorovich lived and worked in

Novosibirsk Novosibirsk is the largest city and administrative centre of Novosibirsk Oblast and the Siberian Federal District in Russia. As of the 2021 Russian census, 2021 census, it had a population of 1,633,595, making it the most populous city in Siber ...

, 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, which he shared with Tjalling Koopmans, 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 ( ...

, 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 (for example, Inner product space#Definition, inner product, Norm (mathematics ...

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 operato ...

. 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 ''i''-th approximation (called an " ...

s, obtaining the Kantorovich inequalities on the convergence rate of the

gradient method In optimization, a gradient method is an algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational ...

and of

Newton's method In numerical analysis, the Newton–Raphson method, also known simply as Newton's 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 ...

(see the Kantorovich theorem). Kantorovich considered

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

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 or probability calculus 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 expre ...

, 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 σ-algebra that satisfies Measure (mathematics), measure properties such as ''countable additivity''. The difference between a probability measure an ...

s. 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, 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 Academic staff of Military Engineering-Technical University Academic staff of Novosibirsk State University Saint Petersburg State University alumni Academic staff of Saint Petersburg State University Nobel laureates in Economics Recipients of the Stalin Prize Recipients of the Lenin Prize 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 Jews Soviet economists Soviet Jews Soviet mathematicians Soviet Nobel laureates Burials at Novodevichy Cemetery Russian scientists

Biography

Mathematics

See also

Notes

References

Further reading

External links