### Abstract

A primal-dual path-following algorithm that applies directly to a linear program of the form, min{c^{t}x{divides}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( {Mathematical expression}ds^{2} 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 language | English |
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Pages (from-to) | 33-52 |

Number of pages | 20 |

Journal | Mathematical Programming |

Volume | 58 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 1993 Jan |

### Keywords

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

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

Choi, I. C., & Goldfarb, D. (1993). Exploiting special structure in a primal-dual path-following algorithm.

*Mathematical Programming*,*58*(1-3), 33-52. https://doi.org/10.1007/BF01581258