In this paper we present the convergence analysis of the inexact infeasible path-following(IIPF) interior point algorithm. In this algorithm the preconditioned conjugate gradient method is used to solve the reduced KKT system (the augmented system). The augmented system is preconditioned by using a block triangular matrix. The KKT system is solved approximately. Therefore, it becomes necessary to study the convergence of interior point method for this specific inexact case. We present the convergence analysis of the inexact infeasible path-following (IIPF) algorithm, prove the global convergence of this method and provide complexity analysis.
MS-2007-03, School of Mathematics, University of Edinburgh, JCMB, King's Buildings, EDINBURGH, EH9 3JZ, UK. 08/2007