Exploiting special structure in a primal-dual path-following algorithm

In Chan Choi, Donald Goldfarb

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

A primal-dual path-following algorithm that applies directly to a linear program of the form, min{ctx{divides}Ax = b, Hx ≤u, x ≥ 0, x ∈ ℝn}, is presented. This algorithm explicitly handles upper bounds, generalized upper bounds, variable upper bounds, and block diagonal structure. We also show how the structure of time-staged problems and network flow problems can be exploited, especially on a parallel computer. Finally, using our algorithm, we obtain a complexity bound of O( {Mathematical expression}ds2 log(nk)) for transportation problems with s origins, d destinations (s <d), and n arcs, where k is the maximum absolute value of the input data.

Original languageEnglish
Pages (from-to)33-52
Number of pages20
JournalMathematical Programming
Volume58
Issue number1-3
DOIs
Publication statusPublished - 1993 Jan 1
Externally publishedYes

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Keywords

  • Interior point method
  • primal-dual path-following algorithm
  • structured linear programs

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Graphics and Computer-Aided Design
  • Software
  • Management Science and Operations Research
  • Safety, Risk, Reliability and Quality
  • Mathematics(all)
  • Applied Mathematics

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