Parallel Semidefinite Programming and Combinatorial Optimization

Benson, Sara

doi:10.1002/9780470053928.ch4

Cited by 1 publication

(2 citation statements)

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“…By introducing parallel processing in the parts where bottlenecks have occurred in conventional software packages, we have also succeeded in making substantial reductions to the overall computation times. We have conducted numerical experiments to compare the performance of SDPARA-C with that of SDPARA [28] and PDSDP [1] in a variety of different problems. From the results of these experiments, we have verified that SDPARA-C exhibits very high scalability.…”

Section: Resultsmentioning

confidence: 99%

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A parallel primal–dual interior-point method for semidefinite programs using positive definite matrix completion

2006

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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 solve SDPs with a large scale matrix variable as well as a large number of equality constraints with a small amount of memory.

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Section: Resultsmentioning

confidence: 99%

“…The second was SDPARA [28]. The third was PDSDP, as used in the numerical experiments of the paper [1], which employs the dual interior-point method on parallel CPUs. In all the experiments apart from those described in section 4.5, the starting point of the interior-point method was chosen to be X = Y = 100I, z = 0.…”

Section: Numerical Experimentsmentioning

confidence: 99%