Leonid Kantorovich
Encyclopedia
Leonid Vitaliyevich Kantorovich (19 January 1912, Saint Petersburg
– 7 April 1986, Moscow
) was a Soviet
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).
After 1939, he became the professor of Military engineering-technical university
(Russian: Военный инженерно-технический университет). During the Siege of Leningrad
, Kantorovich was the professor of VITU of Navy
and 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."
, Kantorovich had important results in functional analysis
, approximation theory
, and operator theory
.
In particular, Kantorovich formulated fundamental results in the theory of normed
vector lattice
s, which are called "K-spaces" in his honor.
Kantorovich showed that functional analysis
could be used in the analysis of iterative method
s, 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 in transportation theory
. His analysis proposed the Kantorovich metric, which is used in probability theory
, in the theory of the weak convergence of probability measure
s.
Saint Petersburg
Saint Petersburg is a city and a federal subject of Russia located on the Neva River at the head of the Gulf of Finland on the Baltic Sea...
– 7 April 1986, Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
) was a Soviet
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and economist
Economist
An economist is a professional in the social science discipline of economics. The individual may also study, develop, and apply theories and concepts from economics and write about economic policy...
, 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.
Biography
Kantorovich was born on 19 January, 1912, to a Russian Jewish family. His father was a doctor practicing in Saint PetersburgSaint Petersburg
Saint Petersburg is a city and a federal subject of Russia located on the Neva River at the head of the Gulf of Finland on the Baltic Sea...
.
Kantorovich worked for the Soviet government. He was given the task of optimizing
Optimization (mathematics)
In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
production in a plywood
Plywood
Plywood is a type of manufactured timber made from thin sheets of wood veneer. It is one of the most widely used wood products. It is flexible, inexpensive, workable, re-usable, and can usually be locally manufactured...
industry. He came up (1939) with the mathematical technique now known as linear programming
Linear programming
Linear programming is a mathematical method for determining a way to achieve the best outcome in a given mathematical model for some list of requirements represented as linear relationships...
, some years before it was reinvented and much advanced by George Dantzig
George Dantzig
George Bernard Dantzig was an American mathematical scientist who made important contributions to operations research, computer science, economics, and statistics....
. 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).
After 1939, he became the professor of Military engineering-technical university
Military Engineering-Technical University
The Saint Petersburg Military Engineering-Technical University , previously known as the Saint Petersburg Nikolaevsky Engineering Academy, was established in 1810 under Alexander I...
(Russian: Военный инженерно-технический университет). During the Siege of Leningrad
Siege of Leningrad
The Siege of Leningrad, also known as the Leningrad Blockade was a prolonged military operation resulting from the failure of the German Army Group North to capture Leningrad, now known as Saint Petersburg, in the Eastern Front theatre of World War II. It started on 8 September 1941, when the last...
, Kantorovich was the professor of VITU of Navy
Military Engineering-Technical University
The Saint Petersburg Military Engineering-Technical University , previously known as the Saint Petersburg Nikolaevsky Engineering Academy, was established in 1810 under Alexander I...
and in charge of safety on the Road of Life
Road of Life
The Road of Life was the ice road transport route across the frozen Lake Ladoga, which provided the only access to the besieged city of Leningrad in the winter months during 1941–1944 while the perimeter in the siege was maintained by the German Army Group North and the Finnish Defence Forces. ...
. 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
Road of Life
The Road of Life was the ice road transport route across the frozen Lake Ladoga, which provided the only access to the besieged city of Leningrad in the winter months during 1941–1944 while the perimeter in the siege was maintained by the German Army Group North and the Finnish Defence Forces. ...
, to ensure the cars did not sink. However, many cars with food for survivors of the siege were destroyed by the German
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....
air-bombings.
For his feat and courage Kantorovich was awarded the Order of the Patriotic War
Order of the Patriotic War
The Order of the Patriotic War is a Soviet military decoration that was awarded to all soldiers in the Soviet armed forces, security troops, and to partisans for heroic deeds during the German-Soviet War, known by the former-Soviet Union as the Great Patriotic War.- History :The Order was...
, and was decorated with the medal For Defense of Leningrad.
Tjalling Koopmans
Tjalling Charles Koopmans was the joint winner, with Leonid Kantorovich, of the 1975 Nobel Memorial Prize in Economic Sciences....
, was given "for their contributions to the theory of optimal allocation of resources."
Mathematics
In mathematical analysisMathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
, Kantorovich had important results in functional analysis
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 and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, approximation theory
Approximation theory
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby...
, and operator theory
Operator theory
In mathematics, operator theory is the branch of functional analysis that focuses on bounded linear operators, but which includes closed operators and nonlinear operators.Operator theory also includes the study of algebras of operators....
.
In particular, Kantorovich formulated fundamental results in the theory of normed
Normed vector space
In mathematics, with 2- or 3-dimensional vectors with real-valued entries, the idea of the "length" of a vector is intuitive and can easily be extended to any real vector space Rn. The following properties of "vector length" are crucial....
vector lattice
Riesz space
In mathematics a Riesz space, lattice-ordered vector space or vector lattice is an ordered vector space where the order structure is a lattice....
s, which are called "K-spaces" in his honor.
Kantorovich showed that functional analysis
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 and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
could be used in the analysis of iterative method
Iterative method
In computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems. A specific implementation of an iterative method, including the termination criteria, is an algorithm of the iterative method...
s, obtaining the Kantorovich inequalities
Kantorovich inequality
In mathematics, the Kantorovich inequality is a particular case of the Cauchy-Schwarz inequality, which is itself a generalization of the triangle inequality....
on the convergence
Convergence
-Mathematics:* Convergence , refers to the notion that some functions and sequences approach a limit under certain conditions* Convergence , the notion that a sequence of transformations come to the same conclusion, no matter what order they are performed in.-Natural sciences:*Convergence ,...
rate of the gradient method and of Newton's method
Newton's method
In numerical analysis, Newton's method , named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots of a real-valued function. The algorithm is first in the class of Householder's methods, succeeded by Halley's method...
.
Kantorovich considered infinite-dimensional optimization
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...
problems, such as the Kantorovich-Monge problem in transportation theory
Transportation theory
In mathematics and economics, transportation theory is a name given to the study of optimal transportation and allocation of resources.The problem was formalized by the French mathematician Gaspard Monge in 1781....
. His analysis proposed the Kantorovich metric, which is used in probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, in the theory of the weak convergence of probability measure
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...
s.
Nobel prize lecture
- Kantorovich, Leonid, "Mathematics in Economics: Achievements, Difficulties, Perspectives", Nobel Prize lecture, December 11, 1975
- "Autobiography: Leonid Kantorovich", Nobel Prize website
Further reading
- Dantzig, GeorgeGeorge DantzigGeorge Bernard Dantzig was an American mathematical scientist who made important contributions to operations research, computer science, economics, and statistics....
, Linear programming and extensions. Princeton University Press and the RAND Corporation, 1963. Cf. p.22 for the work of Kantorovich. - Isbell, J.R.John R. IsbellJohn Rolfe Isbell was an American mathematician, for many years a professor of mathematics at the University of Buffalo .-Biography:...
; Marlow, W.H., "On an Industrial Programming Problem of Kantorovich", Management Science, Vol. 8, No. 1 (Oct., 1961), pp. 13–17 - Koopmans, Tjalling C., "Concepts of optimality and their uses", Nobel Memorial Lecture, December 11, 1975
- Kutateladze, S.S., "The World Line of Kantorovich", Notices of the ISMS, International Society for Mathematical Sciences, Osaka, Japan, January 2007
- Kutateladze, S.S., "Kantorovich's Phenomenon", Siberian Math. J. (Сибирский мат. журн.), 2007, V. 48, No. 1, 3–4, November 29, 2006.
- Kutateladze, S.S., "Mathematics and Economics of Kantorovich" Vershik, AnatolyAnatoly VershikAnatoly Moiseevich Vershik is a Soviet and Russian mathematician. He is most famous for his joint work with Sergey V. Kerov on representations of infinite symmetric groups and applications to the longest increasing subsequences....
, et al., "Leonid V. Kantorovich (1912-1986)", Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. Also published in the Siberian Mathematical Journal, Volume 43 (2002), No. 1, pp. 3–8 Vershik, Anatoly, "On Leonid Kantorovich and linear programming"
External links
(With additional photos.)- Information about: Leonid Vitaliyevich Kantorovich - IDEAS/RePEc