Abstract
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 the 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.
Original language | English |
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Pages (from-to) | 231-247 |
Number of pages | 17 |
Journal | Journal of Optimization Theory and Applications |
Volume | 141 |
Issue number | 2 |
DOIs | |
Publication status | Published - May 2009 |
Keywords
- Inexact interior-point methods
- Linear programming
- Preconditioned conjugate gradients
- Indefinite system
- SYSTEMS
- ALGORITHM