A modification of karmarkar's linear programming algorithm

A modification of Karmarkar's linear programming algorithm that uses a recentered projected gradient approach thereby obviating a priori knowledge of the optimal objective function value and proves that the algorithm converges.

Abstract

We present a modification of Karmarkar's linear programming algorithm. Our algorithm uses a recentered projected gradient approach thereby obviatinga priori knowledge of the optimal objective function value. Assuming primal and dual nondegeneracy, we prove that our algorithm converges. We present computational comparisons between our algorithm and the revised simplex method. For small, dense constraint matrices we saw little difference between the two methods.