When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), attention usually placed on accelerating their convergence by designing appropriate preconditioners, but solver as a black box with standard termination criterion which asks for sufficient reduction of residual system. Such approach often leads unnecessary 'oversolving' equations. In this p...

In this paper, we show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton directions along three different algebraic "paths" that lead to a solution of the Karush-Kuhn-Tucker conditions of a given linear programming ...