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Fast implementation for semidefinite programs with positive matrix completion

Makoto Yamashita(Makoto.Yamashita***at***is.titech.ac.jp)
Kazuide Nakata(nakata.k.ac***at***m.titech.ac.jp)

Abstract: Solving semidefinite programs (SDP) in a short time is the key to managing various mathematical optimization problems in practical time. The matrix-completion primal-dual interior-point method (MC-PDIPM) extracts a structural sparsity of input SDP by factorizing the variable matrices, and it shrinks the computation time. In this paper, we propose a new factorization based on the inverse of the variable matrix to enhance the performance of the MC-PDIPM. We also combine multithreaded parallel computing to resolve the major bottlenecks in the MC-PDIPM. The numerical results show that the new factorization and the multithreaded computing successfully reduce the computation time for the SDPs that posses the structural sparsity.

Keywords: Semidefinite programs, Interior-point methods, Matrix completion, Multithreaded computing

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Optimization Software and Modeling Systems (Parallel Algorithms )

Citation: Research Report B-474, Dept. of Mathematical and Computing Science, Tokyo Institute of Technology

Download: [PDF]

Entry Submitted: 10/25/2013
Entry Accepted: 10/28/2013
Entry Last Modified: 10/25/2013

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