### Abstract

A parallel computational method SDPARA-C is presented for SDPs (semidefinite programs). It combines two methods SDPARA and SDPA-C proposed by the authors who developed a software package SDPA. SDPARA is a parallel implementation of SDPA and it features parallel computation of the elements of the Schur complement equation system and a parallel Cholesky factorization of its coefficient matrix. SDPARA can effectively solve SDPs with a large number of equality constraints; however, it does not solve SDPs with a large scale matrix variable with similar effectiveness. SDPA-C is a primal-dual interior-point method using the positive definite matrix completion technique by Fukuda et al., and it performs effectively with SDPs with a large scale matrix variable, but not with a large number of equality constraints. SDPARA-C benefits from the strong performance of each of the two methods. Furthermore, SDPARA-C is designed to attain a high scalability by considering most of the expensive computations involved in the primal-dual interior-point method. Numerical experiments with the three parallel software packages SDPARA-C, SDPARA and PDSDP by Benson show that SDPARA-C efficiently solves SDPs with a large scale matrix variable as well as a large number of equality constraints with a small amount of memory.

Original language | English |
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Pages (from-to) | 24-43 |

Number of pages | 20 |

Journal | Parallel Computing |

Volume | 32 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2006 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Software
- Theoretical Computer Science
- Hardware and Architecture
- Computer Networks and Communications
- Computer Graphics and Computer-Aided Design
- Artificial Intelligence

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## Cite this

*Parallel Computing*,

*32*(1), 24-43. https://doi.org/10.1016/j.parco.2005.07.002