The Ellipsoid Algorithm
نویسنده
چکیده
The Ellipsoid algorithm was developed by (formerly) Soviet mathematicians (Shor (1970), Yudin and Nemirovskii (1975)). Khachian (1979) proved that it provides a polynomial time algorithm for linear programming. The average behavior of the Ellipsoid algorithm is too slow, making it not competitive with the simplex algorithm. However, the theoretical implications of the algorithm are very important, in particular, providing the first proof that linear programming (and a host of other problems) are in P. The following lecture notes accompanied a course given in 2008. For the 2011 course, this subject was covered in far less details (mostly the geometric view). These notes can serve as supplementary reading for interested students.
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