Mathematical Programming

, Volume 58, Issue 1–3, pp 33–52 | Cite as

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

  • In Chan Choi
  • Donald Goldfarb
Article
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Abstract

A primal-dual path-following algorithm that applies directly to a linear program of the form, min{c t x∣Ax = b, Hx ⩽u, x ⩾ 0,x ∈ ℝ n }, 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(\(\sqrt n \)ds2 log(nk)) fortransportation problems withs origins,d destinations (s <d), andn arcs, wherek is the maximum absolute value of the input data.

Key words

Interior point method primal—dual path-following algorithm structured linear programs 
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Copyright information

© The Mathematical Programming Society, Inc. 1993

Authors and Affiliations

  • In Chan Choi
    • 1
  • Donald Goldfarb
    • 2
  1. 1.Department of Industrial EngineeringThe Wichita State State UniversityWichitaUSA
  2. 2.Department of Industrial Engineering and Operations ResearchColumbia UniversityNew YorkUSA

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