Improving the rate of convergence of interior point methods for linear programming

This paper proposes a procedure for improving the rate of convergence of interior point methods for linear programming. If (x^k) is the sequence generated by an interior point method, the procedure derives an auxiliary sequence (nx^k). Under the suitable assumptions it is shown that the sequence (nx^k) converges superlinearly faster to the solution than (x^k). Application of the procedure to the projective and affine scaling algorithms is discussed and some computational illustration is provided.