### 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 1 |

Externally published | Yes |

### Fingerprint

### 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

### Cite this

*Mathematical Programming*,

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

**Exploiting special structure in a primal-dual path-following algorithm.** / Choi, In Chan; Goldfarb, Donald.

Research output: Contribution to journal › Article

*Mathematical Programming*, vol. 58, no. 1-3, pp. 33-52. https://doi.org/10.1007/BF01581258

}

TY - JOUR

T1 - Exploiting special structure in a primal-dual path-following algorithm

AU - Choi, In Chan

AU - Goldfarb, Donald

PY - 1993/1/1

Y1 - 1993/1/1

N2 - 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

AB - 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

KW - Interior point method

KW - primal-dual path-following algorithm

KW - structured linear programs

UR - http://www.scopus.com/inward/record.url?scp=0027911624&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027911624&partnerID=8YFLogxK

U2 - 10.1007/BF01581258

DO - 10.1007/BF01581258

M3 - Article

AN - SCOPUS:0027911624

VL - 58

SP - 33

EP - 52

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1-3

ER -