The primal-dual algorithm as a constraint-set-manipulation device

Arnold Lent, Yair Censor

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)343-357
Number of pages15
JournalMathematical Programming
Issue number1-3
StatePublished - Mar 1991


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

ASJC Scopus subject areas

  • Software
  • General Mathematics


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