Inventor of the Ellipsoid method
Leonid Genrikhovich Khachiyan was a Soviet and American mathematician and computer scientist.
He was most famous for his ellipsoid algorithm (1979) 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, it has inspired other randomized algorithms for convex programming and is considered a significant theoretical breakthrough.
Early life and education
Khachiyan was born on May 3, 1952, in Leningrad to Armenian parents Genrikh Borisovich Khachiyan, a mathematician and professor of theoretical mechanics, and Zhanna Saakovna Khachiyan, a civil engineer. His grandparents were Karabakh Armenians. His family moved to Moscow in 1961, when he was nine. He received a master’s degree from the Moscow Institute of Physics and Technology. In 1978 he earned his Ph.D. in computational mathematics/theoretical mathematics from the Computer Center of the Soviet Academy of Sciences and in 1984 a D.Sc. in computer science from the same institution.
Career
Khachiyan began his career at the Soviet Academy of Sciences, working as a researcher at the academy’s Computer Center in Moscow. He also worked as an adjunct professor at the Moscow Institute of Physics and Technology. In 1979 he stated: « I am a theoretical mathematician and I’m just working on a class of very difficult mathematical problems. » Khachiyan immigrated to the United States in 1989. He first taught at Cornell University as a visiting professor. In 1990 he joined Rutgers University as a visiting professor. He became professor of computer science at Rutgers in 1992. By 2005, he held the position of Professor II at Rutgers, reserved for those faculty who have achieved scholarly eminence in their discipline.
Ellipsoid method
Khachiyan is best known for his four-page February 1979 paper that indicated how an ellipsoid method for linear programming can be implemented in polynomial time. The paper was translated into several languages and spread around the world unusually quickly. Authors of a 1981 survey of his work noted that it « has caused great excitement and stimulated a flood of technical papers » and was covered by major newspapers. It was originally published without proofs, which were provided by Khachiyan in a later paper published in 1980 and by Peter Gács and Laszlo Lovász in 1981. It was Gács and Lovász who first brought attention to Khachiyan’s paper at the International Symposium on Mathematical Programming in Montreal in August 1979. It was further popularized when Gina Kolata reported it in Science Magazine on November 2, 1979.
Recognition
In 1982 he was awarded the prestigious Fulkerson Prize by the Mathematical Programming Society and the American Mathematical Society for outstanding papers in the area of discrete mathematics, particularly his 1979 article « A polynomial algorithm in linear programming. »
