### Abstract

For semidefinite programming (SDP) problems, traditional primaldual interior-point methods based on conventional matrix operations have an upper limit on the problem size that the computer can handle due to memory constraints. But for a special kind of SDP problem, which is called the banded symmetric semidefinite programming (BSDP) problem, a memoryefficient algorithm, called a structured primal-dual interior-point method, can be applied. The method is based on the observation that both banded matrices and their inverses can be represented in sequentially semi-separable (SSS) form with numerical ranks equal to the half bandwidths of the banded matrices. Moreover, all computation can be done sequentially using the SSS form. Experiments of various problem sizes are performed to verify the feasibility of the proposed method.

Original language | English (US) |
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Title of host publication | Topics in Operator Theory |

Subtitle of host publication | Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008 |

Editors | Joseph A. Ball, Vladimir Bolotnikov, Leiba Rodman, Ilya M. Spitkovsky, J. William Helton |

Publisher | Springer International Publishing |

Pages | 111-141 |

Number of pages | 31 |

ISBN (Print) | 9783034601573 |

DOIs | |

State | Published - 2010 |

Event | 19th International Workshop on Operator Theory and its Applications, IWOTA 2008 - Williamsburg, United States Duration: Jul 22 2008 → Jul 26 2008 |

### Publication series

Name | Operator Theory: Advances and Applications |
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Volume | 202 |

ISSN (Print) | 0255-0156 |

ISSN (Electronic) | 2296-4878 |

### Other

Other | 19th International Workshop on Operator Theory and its Applications, IWOTA 2008 |
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Country | United States |

City | Williamsburg |

Period | 7/22/08 → 7/26/08 |

### Keywords

- Banded matrix
- Interior-point method
- Semidefinite program
- Sequentially semi-separable

### ASJC Scopus subject areas

- Analysis

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## Cite this

*Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008*(pp. 111-141). (Operator Theory: Advances and Applications; Vol. 202). Springer International Publishing. https://doi.org/10.1007/978-3-0346-0158-0_7