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 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 po ...

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 Saint Petersburg State University (SPBGU; ) is a public research university in Saint Petersburg, Russia, and one of the oldest and most prestigious universities in Russia. Founded in 1724 by a decree of Peter the Great, the university from the be ...

. 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 A doctorate (from Latin ''doctor'', meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism '' licentia docendi'' ("licence to teach ...

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

production in a

plywood Plywood is a composite material manufactured from thin layers, or "plies", of wood veneer that have been stacked and glued together. It is an engineered wood from the family of manufactured boards, which include plywood, medium-density fibreboa ...

industry. He devised the mathematical technique now known as

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 dev ...

. 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 The Saint Petersburg Military Engineering-Technical University (Nikolaevsky) (, VITU), previously known as the Saint Petersburg Nikolaevsky Engineering Academy, was established in 1810 under Alexander I. The university is situated in the fo ...

. 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 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 und ...

. 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 German(s) may refer to: * Germany, the country of the Germans and German things **Germania (Roman era) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizenship in Germany, see also Ge ...

airstrikes. For his feat and courage Kantorovich was awarded the

Order of the Patriotic War The Order of the Patriotic War () is a Soviet Union, Soviet military Order (decoration), decoration that was awarded to all soldiers in the Soviet armed forces, security troops, and to Partisan (military), partisans for heroic deeds in the Easte ...

, 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 Novosibirsk State University (NSU) 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 act ...

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

, 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 ( ...

, 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 In mathematical analysis, particularly numerical analysis, the rate of convergence and order of convergence of a sequence that converges to a Limit of a sequence, limit are any of several characterizations of how quickly that sequence approaches ...

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 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 (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 Kuzma Sergeyevich 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 effects ...

, 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 c ...

, 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) and Collabora Online, with Apache OpenOffice being considered mostly d ...

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