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
- asymptotic feasibility
- constraint-set-manipulation
- continuity of value functional
- entropy maximization
- Primal-dual algorithm
ASJC Scopus subject areas
- Software
- Mathematics (all)