A Class of Projective Transformations for Linear Programming

A class of projective transformations under which potential functions are invariant for linear programming is described. As a result, a new projective algorithm converging in $O(L\sqrt n)$ iterations is developed. The algorithm does not require centering conditions, and its convergence speed is improved by a factor $\sqrt n $ over Karmarkar’s projective algorithm and by a constant over the recent affine potential reduction algorithm.