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 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 in 1949 and the
Nobel Memorial Prize in Economic Sciences 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. He was given the task of
optimizing production in a
plywood industry. He devised the mathematical technique now known as
linear programming 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
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, 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
**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, and was decorated with the medal ''For Defense of Leningrad''.
After 1960, Kantorovich lived and worked in
Novosibirsk, 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
In mathematical analysis, 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, norm, topology, etc.) and the linear functions defi ...
, approximation theory, 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
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, norm, topology, etc.) and the linear functions defi ...
could be used in the analysis of iterative method
In computational mathematics, an iterative method is a 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 from the pre ...
s, obtaining the Kantorovich inequalities on the convergence rate of the gradient method In 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 the gradient descent and t ...
and of Newton's method (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 theore ...
).
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 ...
, in the theory of the weak convergence of probability measures.
Image:Kantorovich (Petrov-Vodkin).jpg, Portrait by Petrov-Vodkin
Kuzma Sergeevich Petrov-Vodkin, (; November 5, Old_Style_and_New_Style_dates">O._S._24_October.html" ;"title="Old_Style_and_New_Style_dates.html" ;"title="nowiki/>O._S._24_October">Old_Style_and_New_Style_dates.html"_;"title="nowiki/>Old_Styl ...
. 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.
See also
* List of Russian mathematicians
A ''list'' is any set of items in a row. List or lists may also refer to:
People
* List (surname)
Organizations
* List College, an undergraduate division of the Jewish Theological Seminary of America
* SC Germania List, German rugby union ...
* List of economists
This is an incomplete alphabetical list by surname of notable economists, experts in the social science of economics, past and present. For a history of economics, see the article History of economic thought. Only economists with biographical arti ...
* Shadow price
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
Further reading
* Dantzig, George,
Linear programming and extensions
'. Princeton University Press and the RAND Corporation, 1963. Cf
p.22
for the work of Kantorovich.
* Isbell, J.R.; 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"
* Kutateladze, S.S.
"My Kantorovich"
*
*
*
* Ivan Boldyrev and Till Düppe
Programming the USSR: Leonid V. Kantorovich in context
The British Journal for the History of Science. 2020. 53(2): 255-278.
*
* Kutateladze, S.S., et al.
"Leonid V. Kantorovich (1912–1986)"
Sobolev Institute of Mathematics of the Siberian Division 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.)
– 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