## Abstract

The first two parts of this paper have developed a simplex algorithm for minimizing convex separable piecewise-linear functions subject to linear constraints. This concluding part argues that a direct piecewiselinear simplex implementation has inherent advantages over an indirect approach that relies on transformation to a linear program. The advantages are shown to be implicit in relationships between the linear and piecewise-linear algorithms, and to be independent of many details of implementation. Two sets of computational results serve to illustarate these arguments; the piecewise-linear simplex algorithm is observed to run 2-6 times faster than a comparable linear algorithm, not including any additional expense that might be incurred in setting up the equivalent linear program. Further support for the practical value of a good piecewise-linear programming algorithm is provided by a survey of many varied applications.

Original language | English (US) |
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Pages (from-to) | 213-235 |

Number of pages | 23 |

Journal | Mathematical Programming |

Volume | 53 |

Issue number | 1-3 |

DOIs | |

State | Published - Jan 1 1992 |

## Keywords

- Linear programming
- nondifferentiable optimization
- piecewise-linear programming
- simplex methods

## ASJC Scopus subject areas

- Software
- Mathematics(all)