Convergence Analysis of the Inexact Infeasible Interior-Point Method for Linear Optimization

G. Al-Jeiroudi, J. Gondzio

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)231-247
Number of pages17
JournalJournal of Optimization Theory and Applications
Volume141
Issue number2
DOIs
Publication statusPublished - May 2009

Keywords

  • Inexact interior-point methods
  • Linear programming
  • Preconditioned conjugate gradients
  • Indefinite system
  • SYSTEMS
  • ALGORITHM

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