## Abstract

A general primal-dual algorithm for linearly constrained optimization problems is formulated in which the dual variables are updated by a dual algorithmic operator. Convergence is proved under the assumption that the dual algorithmic operator implies asymptotic feasibility of the primal iterates with respect to the linear constraints. A general result relating the minimal values of an infinite sequence of constrained problems to the minimal value of a limiting problem (constrained by the limit of the sequence of constraints sets) is established and invoked. The applicability of the general theory is demonstrated by analyzing a specific dual algorithmic operator. This leads to the "MART" algorithm for constrained entropy maximization used in image reconstruction from projections.

Original language | English |
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Pages (from-to) | 343-357 |

Number of pages | 15 |

Journal | Mathematical Programming |

Volume | 50 |

Issue number | 1-3 |

DOIs | |

State | Published - Mar 1991 |

## Keywords

- Primal-dual algorithm
- asymptotic feasibility
- constraint-set-manipulation
- continuity of value functional
- entropy maximization

## ASJC Scopus subject areas

- Software
- General Mathematics