Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming
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HPCES005.pdf
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176.07 KB
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Checksum (MD5)
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Author(s)
Chai, Joo-Siong
Toh, Kim Chuan
Date Issued
January 2005
Series/Report no.
High Performance Computation for Engineered Systems (HPCES);
Abstract
We study the preconditioning of symmetric indefinite linear systems of equations that arise in interior point solution of linear optimization problems. The preconditioning method that we study exploits the block structure of the augmented matrix to design a similar block structure preconditioner to improve the spectral properties of the resulting preconditioned matrix so as to improve the convergence rate of the iterative solution of the system. We also propose a two-phase algorithm that takes advantage of the spectral properties of the transformed matrix to solve for the Newton directions in the interior-point method. Numerical experiments have been performed on some LP test problems in the NETLIB suite to demonstrate the potential of the preconditioning method discussed.
Subjects
preconditioning
linear optimization
iteration
symmetric indefinite linear systems
interior point solutions
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