## Abstract

In this paper we introduce a primal-dual affine scaling method. The method uses a search-direction obtained by minimizing the duality gap over a linearly transformed conic section. This direction neither coincides with known primal-dual affine scaling directions (Jansen et al., 1993; Monteiro et al., 1990), nor does it fit in the generic primal-dual method (Kojima et al., 1989). The new method requires O(√n L) main iterations. It is shown that the iterates follow the primal-dual central path in a neighbourhood larger than the conventional script N sign_{2} neighbourhood. The proximity to the primal-dual central path is measured by trigonometric functions.

Original language | English (US) |
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Pages (from-to) | 177-194 |

Number of pages | 18 |

Journal | Mathematical Programming, Series B |

Volume | 72 |

Issue number | 2 |

State | Published - Feb 1996 |

## Keywords

- Affine scaling
- Linear programming
- Polynomiality
- Primal-dual interior point algorithm