## Abstract

In order to minimize a closed convex function that is approximated by a sequence of better behaved functions, we investigate the global convergence of a general hybrid iterative algorithm, which consists of an inexact relaxed proximal point step followed by a suitable orthogonal projection onto a hyperplane. The latter permits to consider a fixed relative error criterion for the proximal step. We provide various sets of conditions ensuring the global convergence of this algorithm. The analysis is valid for nonsmooth data in infinite-dimensional Hilbert spaces. Some examples are presented, focusing on penalty/barrier methods in convex programming. We also show that some results can be adapted to the zero-finding problem for a maximal monotone operator.

Original language | English |
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Pages (from-to) | 966-984 |

Number of pages | 19 |

Journal | Mathematics of Operations Research |

Volume | 30 |

Issue number | 4 |

DOIs | |

State | Published - Nov 2005 |

Externally published | Yes |

## Keywords

- Diagonal iteration
- Global convergence
- Hybrid method
- Parametric approximation
- Proximal point