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	In Memoriam: Leonid Khachiyan
		Leonid G. Khachiyan of South Brunswick, N.J., professor of computer science at Rutgers, The State University of New Jersey, died suddenly of a heart attack on Friday, April 29 at the age of 52.
		Khachiyan's 1979 Doklady paper was but his fourth in a long list of single and co-authored publications in diverse areas of algorithms, computational complexity and applications.
		Khachiyan is survived by his wife of 20 years Olga Pischikova Reynberg and daughters Anna, a sophomore at Rutgers, and Nina, who plans to attend Rutgers in the fall.
	www.cs.rutgers.edu /Khachiyan (563 words)

	Leonid_Khachiyan (Site not responding. Last check: 2007-10-30)
		Of Armenian descent, Khachiyan was born in St.
		After coming to the States, Khachiyan's work continued some of its old themes, like his work on the complexity of maximal volume inscribed ellipsoids and his fascinating paper on rounding polytopes, and added some new ones.
		Khachiyan is survived by his wife of 20 years and two daughters.
	en.filepoint.de /info/Leonid_Khachiyan (324 words)

	Technology Review: Obituary: Mystery Man
		Leonid Khachiyan, a Russian mathematician and a professor at Rutgers University who published a groundbreaking theorem in 1979 that helped advance the field of linear programming, died April 29 at the age of 52.
		Khachiyan's breakthrough, applying an approach known as the ellipsoid method to linear programming, continues to aid computer scientists in their efforts to tackle the enormously complex challenges of scheduling and resource allocation in fields ranging from finance to telecommunications to the airline industry.
		When Khachiyan first published his work on the ellipsoid method, he was a little-known 27-year-old mathematician studying computational mathematics at the Computing Center of the Soviet Academy of Sciences in Moscow.
	www.technologyreview.com /read_article.aspx?id=14772&ch=infotech (268 words)

	Leonid Khachiyan Is Dead at 52; Advanced Computer Math - New York Times
		Leonid Khachiyan, a Russian-born mathematician who helped to advance the field of linear programming, which is used by computer scientists to schedule complex rosters of airline flights and to solve problems in finance and industry, died on April 29 at his home in South Brunswick, N.J. He was 52.
		Khachiyan's algorithm was reported in The New York Times in 1979 and received widespread acclaim for its ingenuity.
		Dr. Khachiyan is survived by his wife, the former Olga Reynberg; two daughters, Anna and Nina, also of South Brunswick; and, in Moscow, his father, Genrikh; his mother, Zhanna; and two brothers, Boris and Eugene.
	www.dcis.rutgers.edu /cs/Khachiyan/articles/nytimes/index.html (437 words)

	Leonid Khachiyan Information
		Leonid Khachiyan (May 3, 1952 – April 29, 2005) was a Russian-born mathematician who taught Computer Science at Rutgers University.
		He was most famous for his Ellipsoid algorithm for linear programming, which was the first such algorithm known to have a polynomial running time.
		Even though this algorithm was shown to be impractical due to the high degree of the polynomial in its running time, it has inspired other randomized algorithms for convex programming and is considered a significant theoretical breakthrough.
	www.bookrags.com /Leonid_Khachiyan (318 words)

	SIAM 2005 Optimization Conference
		Khachiyan was best known for his 1979 use of the ellipsoid algorithm, originally developed for convex programming, to give the first polynomial-time algorithm to solve linear programming problems.
		Khachiyan's analysis led to broad applications of the ellipsoid algorithm as a method of obtaining complexity results for discrete optimization problems.
		Khachiyan and co-authors also developed polynomial-time algorithms for convex quadratic programming, studied the complexity of polynomial programming over the reals and the integers, and devised the method of inscribed ellipsoids for general convex programming.
	www.siam.org /meetings/op05 (291 words)

	DBLP: Leonid Khachiyan
		Leonid Khachiyan, Endre Boros, Konrad Borys, Khaled M. Elbassioni, Vladimir Gurvich, Kazuhisa Makino: Enumerating Spanning and Connected Subsets in Graphs and Matroids.
		Leonid Khachiyan, Endre Boros, Konrad Borys, Khaled M. Elbassioni, Vladimir Gurvich: Generating all vertices of a polyhedron is hard.
		Leonid Khachiyan, Endre Boros, Khaled M. Elbassioni, Vladimir Gurvich: Generating All Minimal Integral Solutions to Monotone and, or-Systems of Linear, Transversal and Polymatroid Inequalities.
	www.vldb.org /dblp/db/indices/a-tree/k/Khachiyan:Leonid.html (797 words)

	Leonid Khachiyan - Definition, explanation
		Leonid Khachiyan (May 3, 1952 - April 29, 2005) was a Russian-born mathematician who taught Computer Science at Rutgers University.
		Of Armenian descent, Khachiyan was born in St. Petersburg and moved to Moscow with his parents at age 9 where he later earned a Ph.D. in computational mathematics in 1978 and a D.Sc.
		He is also survived by his father, a retired professor of theoretical mechanics, his mother, a retired civil engineer, and two brothers, all who live in Moscow.
	www.calsky.com /lexikon/en/txt/l/le/leonid_khachiyan.php (285 words)

	leonid meteor showers information -- leonid meteor showers (Site not responding. Last check: 2007-10-30)
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	www.ismsshowers.info /leonidmeteorshowers (1244 words)

	Leonid Khachiyan: Rutgers computer scientist dies (Site not responding. Last check: 2007-10-30)
		RUTGERS -- Leonid G. Khachiyan of South Brunswick, a Rutgers University professor of computer science whose work in his native Soviet Union in 1979 "rocked the world of computer analysis," died Friday of a heart attack.
		Khachiyan, of Armenian descent, was born in Leningrad in 1952, and moved to Moscow with his parents at age 9.
		Khachiyan is survived by his wife of 20 years, Olga Pischikova Reynberg, and daughters Anna, a sophomore at Rutgers, and Nina, who plans to attend Rutgers in the fall, according to the university's Office of Media Relations.
	www.cs.rutgers.edu /Khachiyan/articles/homenews.html (619 words)

	DBLP: Endre Boros
		Leonid Khachiyan, Endre Boros, Khaled Elbassioni, Vladimir Gurvich, Kazuhisa Makino: Enumerating disjunctions and conjunctions of paths and cuts in reliability theory.
		Leonid Khachiyan, Endre Boros, Khaled Elbassioni, Vladimir Gurvich: An efficient implementation of a quasi-polynomial algorithm for generating hypergraph transversals and its application in joint generation.
		Leonid Khachiyan, Endre Boros, Konrad Borys, Khaled M. Elbassioni, Vladimir Gurvich, Kazuhisa Makino: Generating Cut Conjunctions and Bridge Avoiding Extensions in Graphs.
	dblp.uni-trier.de /db/indices/a-tree/b/Boros:Endre.html (1479 words)

	SIAM: Leonid Khachiyan, 1952—2005: An Appreciation
		Leonid Khachiyan died of a heart attack on April 29, a few days before his 53rd birthday, in South Brunswick, New Jersey.
		Because the algorithm was designed for the real-number model, and required an estimate of the distance to an optimal solution, Khachiyan had to establish a number of bounds on sizes of solutions, volumes of polyhedra, and the precision required to carry out the computations to achieve his goal.
		Leonid Khachiyan was a great scholar and a much-loved father, husband, and friend.
	www.siam.org /news/news.php?id=197 (1841 words)

	Computational Complexity: Leonid Khachiyan (1952-2005)
		Leonid Khachiyan passed away Friday at the age of 52.
		While the simplex algorithm solved LP well in practice, Khachiyan gave the first formal proof of an efficient algorithm in the worst case.
		Khachiyan's method is believed to offer an approach for the linear programming of computers to solve so-called "traveling salesman" problems.
	weblog.fortnow.com /2005/05/leonid-khachiyan-1952-2005.html (479 words)

	Leonid Khachiyan, professor, leading computer scientist - The Boston Globe
		Leonid G. Khachiyan, a renowned professor of computer science at Rutgers University whose work helped solve how computers process large problems, died of a heart attack Friday.
		Khachiyan proved the existence of an efficient way to solve programming problems thought to be intractable because they dealt with an often astronomically large number of options.
		Khachiyan came to the United States in 1989.
	www.boston.com /news/globe/obituaries/articles/2005/05/05/leonid_khachiyan_professor_leading_computer_scientist?mode=PF (206 words)

	Leonid Khachiyan - Education - Information - Educational Resources - Encyclopedia - Music
		Leonid Khachiyan is a Russian born mathematician who currently teaches Computer Science at Rutgers University.
		He is most famous for his Ellipsoid algorithm for linear programming, that was the first such algorithm known to have a polynomial running time.
		Khachiyan lives in South Brunswick, New Jersey, with his wife and two daughters.
	www.music.us /education/L/Leonid-Khachiyan.htm (318 words)

	Leonid Khachiyan (Site not responding. Last check: 2007-10-30)
		Leonid Khachiyan is a Russian born mathematician who currently teaches Computer Science at Rutgers University.
		He is most famous for his Ellipsoid algorithm for linear programming, that was the first such algorithm known to have a polynomial running time.
		Khachiyan lives in South Brunswick, New Jersey, with his wife and two daughters, and one cat.
	www.33beat.com /Leonid_Khachiyan.html (416 words)

	SIAM: Optimization Community Mourns Loss of Two Linear Programming Giants
		Leonid Khachiyan, a professor of computer science at Rutgers University, died suddenly on April 29, days short of his 53rd birthday.
		Born in Russia (in what is now St. Petersburg), Khachiyan lived for many years in Moscow, where he received doctoral degrees in computational mathematics (1978) and computer science (1984) at the Computing Center of the USSR Academy of Sciences.
		Khachiyan's analysis, the piece continues, "led to broad applications of the ellipsoid algorithm as a method for obtaining complexity results for discrete optimization problems.
	www.siam.org /news/news.php?id=110 (535 words)

	Our Daily Dead » Blog Archive » Leonid Khachiyan Is Dead at 52; Advanced Computer Math - Celebrating Life ...
		Dr. Khachiyan (pronounced KA-tchee-an), who began his career at the Russian Academy of Sciences in Moscow, had been a professor of computer science at Rutgers since 1992.
		In his paper “A Polynomial Algorithm in Linear Programming,”; Dr. Khachiyan proposed using an ellipsoid algorithm in approaching theoretical problems believed to be too demanding for the simplex method, and “turned the field on its head,” said Dr. Michael D. Grigoriadis, a professor of computer science at Rutgers.
		This entry was posted on Monday, May 23rd, 2005 at 12:00 am and is filed under ODD Guests.
	www.ourdailydead.com /leonid-khachiyan.htm (371 words)

	Linear programming Summary
		The first worst-case polynomial-time algorithm for the linear programming problem was proposed by Leonid Khachiyan in 1979.
		It was based on the ellipsoid method in nonlinear optimization by Naum Shor, which is the generalization of the ellipsoid method in convex optimization by Arkadi Nemirovski, a 2003 John von Neumann Theory Prize winner, and D.
		However, the practical performance of Khachiyan's algorithm is disappointing: generally, the simplex method is more efficient.
	www.bookrags.com /Linear_programming (2246 words)

	Citations: A Polynomial algorithm in linear programming - Khachiyan (ResearchIndex) (Site not responding. Last check: 2007-10-30)
		Khachiyan, L. A polynomial algorithm in linear programming.
		Khachiyan, A polynomial algorithm in linear programming, (in Russian), Doklady Akedamii Nauk SSSR, 244, 1093--1096, 1979.
		Khachiyan, L.G., "A polynomial algorithm for linear programming", Doklady Akademiia Nauk SSSR, 244:S, 1979, pp.
	citeseer.ist.psu.edu /context/9577/0 (321 words)

	During the summer of 2002
		George B. Dantzig, professor emeritus of operations research and computer science at Stanford University, and Leonid Khachiyan, professor of computer science at Rutgers University died within two weeks of each other.
		Dantzig invented the field of linear programming and devised the "simplex method." Prof.
		Khachiyan developed the first polynomial-time algorithm for the solution of linear programming problems.
	academic.udayton.edu /josephlang/summer2005.htm (308 words)

	Leonid - Leonid Vitaliyevich Kantorovich - Autobiography (Site not responding. Last check: 2007-10-30)
		Leonid Ilyich Brezhnev, leader of one of the two most powerful nations in the world, was born to Russian parents in the Ukrainian mining town of Kamensk in
		The Leonids are famous because their meteor showers, or storms, can be among the most spectacular.
		The Sveriges Riksbank Prize in Economic Leonid Vitaliyevich Kantorovich I was born in Petersburg (Leningrad) on 19th
	leonid.siteslinks.com (298 words)

	Linear programming (Site not responding. Last check: 2007-10-30)
		The First worst-case polynomial-time algorithm for the linear programming problem was proposed by Leonid Khachiyan in 1979.
		It was based on the ellipsoid method in nonlinear optimization by Naum Shor, which is the generalization of the ellipsoid method in convex optimization by Arkadi Nemirovski, a 2003 John von Neumann Theory Prize winner, and D. Yudin.
		However, the practical performance of Khachiyan's algorithm is disappointing: generally, the simplex method is more efficient.
	linear-programming.iqnaut.net (1043 words)

	Leonid Khachiyan, 52; Computer Science Expert at Rutgers (Site not responding. Last check: 2007-10-30)
		Leonid Khachiyan, 52; Computer Science Expert at Rutgers
		In 1982, Khachiyan was awarded the Fulkerson Prize from the Mathematical Programming Society and the American Mathematical Society.
		Khachiyan was born in the former Soviet Union in what is now St.
	www.cs.rutgers.edu /Khachiyan/articles/latimes.html (115 words)

	Khaled Elbassioni, my homepage
		(Invited contribution) (with Endre Boros, Konrad Borys, Vladimir Gurvich and Leonid Khachiyan).
		(with Endre Boros, Konrad Borys, Vladimir Gurvich and Leonid Khachiyan).
		(with Endre Boros, Konrad Borys, Vladimir Gurvich, Leonid Khachiyan and Kazuhisa Makino).
	www.mpi-sb.mpg.de /~elbassio (600 words)

	Yuki Saka (Site not responding. Last check: 2007-10-30)
		This summer I am working with my advisor, Professor Leonid Khachiyan.
		We study combinatorial properties and enumeration algorithm of generalized cuts and spanning subgraphs.
		[3] E. Boros, K. Elbassioni, V. Gurvich, L. Khachiyan, An inequality for polymatroid functions and its applications.
	dimacs.rutgers.edu /~ysaka (360 words)

	Untitled Document
		In 1979 Leonid G. Khachiyan employed, in a very surprising way, the Ellipsoid Method to prove that linear programs can be solved in polynomial time, a result that has triggered intensified interest in LP algorithms.
		Leonid Khachiyan died on 29 April, aged 52, and George Dantzig on 13 May, aged 90.
		They both will be remembered forever for their contributions to optimization theory and practice.
	www.lms.ac.uk /newsletter/339/339_05.html (715 words)

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