Naum Z. Shor

Naum Zuselevich Shor
Born	1 January 1937(1937-01-01) Kiev, Ukraine, USSR
Died	26 February 2006(2006-02-26) (aged 69)
Nationality	Soviet Union  Ukraine
Institutions	V.M. Glushkov Institute of Cybernetics, Kiev, Ukraine

Naum Zuselevich Shor (Russian: Шор Наум Зуселевич) (1 January 1937 – 26 February 2006) was a Soviet and Ukrainian Jewish mathematician specializing in optimization.

He made significant contributions to nonlinear and stochastic programming, numerical techniques for non-smooth optimization, discrete optimization problems, matrix optimization, dual quadratic bounds in multi-extremal programming problems.

Shor became a full member of the National Academy of Science of Ukraine in 1998.

Subgradient methods

Main article: Subgradient method

See also: Ellipsoid method, Linear programming, Convex optimization, Computational complexity, and Iterative method

N. Z. Shor is well known for his method of generalized gradient descent with space dilation in the direction of the difference of two successive subgradients (the so-called r-algorithm), that was created in collaboration with Nikolay G. Zhurbenko.^{[1] [2]} The ellipsoid method was re-invigorated by A.S. Nemirovsky and D.B. Yudin, who developed a careful complexity analysis of its approximation properties for problems of convex minimization with real data. However, it was Leonid Khachiyan who provided the rational-arithmetic complexity analysis, using an ellipsoid algorithm, that established that linear programming problems can be solved in polynomial time.

It has long been known that the ellipsoidal methods are special cases of these subgradient-type methods.

r-algorithm

Schor's r-algorithm is for unconstrained minimization of (possibly) non-smooth functions^[3], which has been somewhat popular despite an unknown convergence rate. ^[4] It can be viewed as a Quasi-Newton method, although it does not satisfy the secant equation. Although the method involves subgradients, it is distinct from his so-called subgradient method described above.

References

Notes

1. ^ N. Z. Shor and N. G. Zhurbenko, "The minimization method using space dilatation in direction of difference of two sequential gradients," Kibernetika, No. 3, 51-59 (1971).
2. ^ Free implementations of r-algorithm (made by workers of Department Methods for solving complex optimization problems led for a long time by N. Z. Shor) are available in
   • SolvOpt
   • ralg from OpenOpt framework.
3. ^ N.Z. Shor. Minimization Methods for Non-differentiable Functions. Springer-Verlag, New York, 1985.
4. ^ "The Speed of Shor's R-Algorithm", available at http://www.optimization-online.org/DB_HTML/2007/05/1656.html

Bibliography

• "Congratulations to Naum Shor on his 65th birthday", Journal of Global Optimization 24 (2): 111–114, 2002, doi:10.1023/A:1020215832722 .

External links

• ORB Newsletter Issue 5 contains an article with a short biography

Persondata
Name	Shor, Naum Z.
Alternative names
Short description
Date of birth	1 January 1937
Place of birth	Kiev, Ukraine, USSR
Date of death	26 February 2006
Place of death

This article about a European mathematician is a stub. You can help Wikipedia by expanding it.v · Categories: Numerical analysts Operations researchers Theoretical computer scientists Mathematical analysts Ukrainian mathematicians Soviet computer scientists Alumni of Taras Shevchenko National University of Kyiv Moscow Institute of Physics and Technology faculty Members of the National Academy of Sciences of Ukraine USSR State Prize winners 1937 births 2006 deaths Ukrainian Jews Ukrainian people stubs European scientist stubs European mathematician stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем написать реферат Jessica King Muellerius capillaris Look at other dictionaries: Naum Schor — (ukrainisch Наум Зуселевич Шор/Naum Susselewytsch Schor, meist in englischer Transkription zitiert als Naum Z. Shor; * 1. Januar 1937 in Kiew; † 26. Februar 2006) war ein sowjetisch ukrainischer Mathematiker, der sich mit Optimierung… …   Deutsch Wikipedia Naum — may refer to: People Naum Akhiezer, Soviet mathematician Naum Gabo, Russian sculptor Naum Idelson, Soviet astronomer Naum Kleiman, historian of cinema Naum Krasner, Russian mathematician and economist Naum Levin, Ukrainian–Australian chess master …   Wikipedia Shor — may refer to: * Shor film, 1971 Hindi movie * Shor people, an indigenous ethnic group of southern Siberia * Shor language, one of the Turkic languages * Shor s algorithm, quantum algorithm for factoring a number N in O((log N)3) time and O(log N) …   Wikipedia Shor — ist der Name folgender Personen: Dan Shor (* 1956), US amerikanischer Schauspieler, Regisseur und Drehbuchautor Naum Schor (1937–2006), sowjetisch ukrainischer Mathematiker Peter Shor (* 1959), US amerikanischer Mathematiker Shor ist auch der… …   Deutsch Wikipedia Шор, Наум Зуселевич — Наум Зуселевич Шор укр. Наум Зуселевич Шор Дата рождения: 1 января 1937(1937 01 01) Место рождения: Киев, Украинская ССР …   Википедия Subgradient method — Subgradient methods are algorithms for solving convex optimization problems. Originally developed by Naum Z. Shor and others in the 1960s and 1970s, subgradient methods can be used with a non differentiable objective function. When the objective… …   Wikipedia Optimisation linéaire — En optimisation, qui est une branche des mathématiques, un problème d optimisation linéaire est un problème d optimisation dans lequel on minimise une fonction linéaire sur un polyèdre convexe. La fonction coût et les contraintes peuvent donc… …   Wikipédia en Français Linear programming — (LP, or linear optimization) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships.… …   Wikipedia Optimization (mathematics) — In mathematics, the term optimization, or mathematical programming, refers to the study of problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an… …   Wikipedia Ellipsoid method — The ellipsoid method is an algorithm for solving convex optimization problems. It was introduced by Naum Z. Shor, Arkady Nemirovsky, and David B. Yudin in 1972, and used by Leonid Khachiyan to prove the polynomial time solvability of linear… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”