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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… (More)

- Ghussoun Al-Jeiroudi, Jacek Gondzio, J. A. Julian Hall
- Optimization Methods and Software
- 2008

We discuss the use of preconditioned conjugate gradients method for solving the reduced KKT systems arising in interior point algorithms for linear programming. The (indefinite) augmented system form of this linear system has a number of advantages, notably a higher degree of sparsity than the (positive definite) normal equations form. Therefore we use the… (More)

We discuss the use of preconditioned conjugate gradients method for solving the reduced KKT systems arising in interior point algorithms for linear programming. The (indefinite) augmented system form of this linear system has a number of advantages, notably a higher degree of sparsity than the (positive definite) normal equations form. Therefore we use the… (More)

In each iteration of the interior point method (IPM) at least one linear system has to be solved. The main computational effort of IPMs consists in the computation of these linear systems. Solving the corresponding linear systems with a direct method becomes very expensive for large scale problems. In this thesis, we have been concerned with using an… (More)

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