A Path-Following Projective Interior Point Method for Linear Programming

Abstract

In this paper the authors present a projective interior point method which follows the “central trajectory” and finds an optimal solution in at most $O( \sqrt{n} L )$ iterations. This algorithm is essentially Anstreicher’s variant of Karmarkar’s projective algorithm with a weakened “ball update” for lower bounds. The result indicates that a strong relationship exists between projective and path-following algorithms. The authors show that within a certain probabilistic framework the expected number of iterations required by their algorithm is $O( L )$.