A unified framework for primal-dual methods in minimum cost network flow problems

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30 Scopus citations

Abstract

We introduce a broad class of algorithms for finding a minimum cost flow in a capacitated network. The algorithms are of the primal-dual type. They maintain primal feasibility with respect to capacity constraints, while trying to satisfy the conservation of flow equation at each node by means of a wide variety of procedures based on flow augmentation, price adjustment, and ascent of a dual functional. The manner in which these procedures are combined is flexible thereby allowing the construction of algorithms that can be tailored to the problem at hand for maximum effectiveness. Particular attention is given to methods that incorporate features from classical relaxation procedures. Experimental codes based on these methods outperform by a substantial margin the fastest available primal-dual and primal simplex codes on standard benchmark problems.

Original languageEnglish (US)
Pages (from-to)125-145
Number of pages21
JournalMathematical Programming
Volume32
Issue number2
DOIs
StatePublished - Jun 1985
Externally publishedYes

Keywords

  • Network Flow
  • Out-of-Kilter
  • Primal-Dual
  • Relaxation

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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