Name
Title | ||
|---|---|---|
A parallel primal-dual interior-point method for semidefinite programs using positive definite matrix completion |
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. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.parco.2005.07.002 | Parallel Computing |
Keywords | Field | DocType |
coefficient matrix,parallel implementation,parallel primal-dual interior-point method,large scale matrix variable,parallel computation,pc cluster,sdpara-c benefit,parallel computational method,primal-dual interior-point method,numerical experiment,semidefinite program,positive definite matrix completion,large number,primal–dual interior-point method,parallel cholesky factorization,equality constraint,positive definite matrix,cholesky factorization,schur complement,parallel computer | Mathematical optimization,Coefficient matrix,Computer science,Positive-definite matrix,Parallel computing,Software,Interior point method,Schur complement,Cholesky decomposition,Scalability,Computation | Journal |
Volume | Issue | ISSN |
32 | 1 | Parallel Computing |
Citations | PageRank | References |
11 | 1.66 | 19 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kazuhide Nakata | 1 | 216 | 24.12 |
| Makoto Yamashita | 2 | 136 | 13.74 |
| Katsuki Fujisawa | 3 | 248 | 28.63 |
| Masakazu Kojima | 4 | 1603 | 222.51 |