where e e IR", b e IR" and A is an m x n matrix. In the last four years there has been a vast amount of work on "interior point" algorithms, motivated by Karmarkar's algorithm [16]. Unlike the traditional simplex method which moves from vertex to vertex around the feasible region {x;>4x > b}, interior point methods proceed through the interior {x;Ax > b] of the feasible region. Karmarkar's algo...

In this paper we present a generic projective interior point algorithm for linear programming which includes modiied versions of Karmarkar's original algorithm and most other projective algorithms that have been proposed as special cases. We show that this class of algorithms has a worst case iteration bound of O(p nL) and is closely related to the class of potential reduction interior point me...