Narendra Karmarkar

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Narendra K. Karmarkar (b. 1957) is an Indian mathematician, renowned for developing Karmarkar's algorithm.

Karmarkar received his B.Tech at the IIT Bombay in 1978. Later, he received his M.S. at the California Institute of Technology, and his Ph.D. at the Institute of Computer Science at the University of California, Berkeley. He published his famous result in 1984 while he was working for Bell Laboratories in New Jersey. Karmarkar was a professor at the Tata Institute of Fundamental Research in Bombay. In 2006, he started a company, with funding from Mr. Ratan Tata to the tune of INR 400 crore (US$ 80 Million), in the field of High Performance Computing [1]. However, he has since abandoned the company over differences with the Tata group concerning the basic objectives behind the project [2].

[edit] Karmarkar's algorithm

Main article: Karmarkar's algorithm

Karmarkar's algorithm solves linear programming problems in polynomial time. These problems are represented by "n" variables and "m" constraints. The previous method of solving these problems consisted of problem representation by an "x" sided solid with "y" vertices, where the solution was approached by traversing from vertex to vertex. Karmarkar's novel method approaches the solution by cutting through the above solid in its traversal. Consequently, complex optimization problems are solved much faster using the Karmarkar algorithm. A practical example of this efficiency is the solution to a complex problem in communications network optimization where the solution time was reduced from weeks to days. His algorithm thus enables faster business and policy decisions. Karmarkar's algorithm has stimulated the development of several other interior point methods, some of which are used in current codes for solving linear programs.

[edit] Awards (selected)

Karmarkar received a number of awards for his algorithm, among them:

Distinguished Alumnus Award, Computer Science and Engineering, University of California, Berkeley (1993)
Ramanujan Prize for Computing, given by Asian Institute Informatics (1989)
Fulkerson Prize in Discrete Mathematics given jointly by the American Mathematical Society & Mathematical Programming Society (1988)
Fellow of Bell Laboratories (1987- )
Texas Instruments Founders’ Prize (1986)
Marconi International Young Scientist Award (1985)
Frederick W. Lanchester Prize of the Operations Research Society of America for the Best Published Contributions to Operations Research (1984)
National Science Talent Award in Mathematics, India (1972, India)

The Association for Computing Machinery awarded him the prestigious Paris Kanellakis Award in 2000 for his work. The award citation reads:

For his theoretical work in devising an Interior Point method for linear programming that provably runs in polynomial time, and for his implementation work suggesting that Interior Point methods could be effective for linear programming in practice as well as theory. Together, these contributions inspired a renaissance in the theory and practice of linear programming, leading to orders of magnitude improvement in the effectiveness of widely-used commercial optimization codes.