On Karmakar's Algorithm for Linear Programming

This paper deals with the convergence of the new polynomial-time algorithm developed by N.Karmakar and its relationship with thickness of concentric ellipsoids. Herein, we generalize the Karmakar'sinequality to discuss the bounds of objective function and obtain refind form of Karmakar's Formula for thespeed of convergence and convergence ration Karmakar's algorithm admits linear convergence in general andsupper linear convergence in special case which hopelessly turn out to be trivial. We also show the super linearconvergence of the sequence of the values of the objective function at different points of the polytope