Abstract
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.
Key words:
Inexact Interior Point Method, Preconditioned Indefinite System,
Infeasible Interior Point Algorithm, Linear Optimization.