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

Kazuhide Nakata, Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima

Research output: Contribution to journalArticle

17 Citations (Scopus)

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 languageEnglish
Pages (from-to)24-43
Number of pages20
JournalParallel Computing
Volume32
Issue number1
DOIs
Publication statusPublished - Jan 1 2006
Externally publishedYes

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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