### Abstract

In this paper, we give an example of a semidefinite programming problem in which primal-dual affine-scaling algorithms using the HRVW/KSH/M, MT, and AHO directions fail. We prove that each of these algorithms can generate a sequence converging to a non-optimal solution and that, for the AHO direction, even its associated continuous trajectory can converge to a non-optimal point. In contrast with these directions, we show that the primal-dual affine-scaling algorithm using the NT direction for the same semidefinite programming problem always generates a sequence converging to the optimal solution. Both primal and dual problems have interior feasible solutions and unique optimal solutions which satisfy strict complementarity, and are nondegenerate everywhere.

Original language | English (US) |
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Pages (from-to) | 149-175 |

Number of pages | 27 |

Journal | Mathematics of Operations Research |

Volume | 24 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1999 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Computer Science Applications
- Management Science and Operations Research

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## Cite this

*Mathematics of Operations Research*,

*24*(1), 149-175. https://doi.org/10.1287/moor.24.1.149