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Augmentation preconditioning for saddle point systems arising from interior point methods Rees, Tim
Abstract
We investigate a preconditioning technique applied to the problem of solving linear systems arising from primal-dual interior point algorithms in linear and quadratic programming. The preconditioner has the attractive property of improved eigenvalue clustering with increased ill-conditioning of the (1,1) block of the saddle point matrix. We demonstrate performance of the preconditioner on problems from the NETLIB and CUTEr test suites. The numerical experiments include results based on inexact inner iterations, and comparisons of the proposed techniques with constraint preconditioners. Approximations to the preconditioner are considered for systems with simple (1,1) blocks. The preconditioning approach is also extended to deal with stabilized systems. We show that for stabilized saddle point systems a minimum residual Krylov method will converge in just two iterations.
Item Metadata
Title |
Augmentation preconditioning for saddle point systems arising from interior point methods
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2006
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Description |
We investigate a preconditioning technique applied to the problem of solving linear systems arising from primal-dual interior point algorithms in linear and quadratic programming. The preconditioner has the attractive property of improved eigenvalue clustering with increased ill-conditioning of the (1,1) block of the saddle point matrix. We demonstrate performance of the preconditioner on problems from the NETLIB and CUTEr test suites. The numerical experiments include results based on inexact inner iterations, and comparisons of the proposed techniques with constraint preconditioners. Approximations to the preconditioner are considered for systems with simple (1,1) blocks. The preconditioning approach is also extended to deal with stabilized systems. We show that for stabilized saddle point systems a minimum residual Krylov method will converge in just two iterations.
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Genre | |
Type | |
Language |
eng
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Date Available |
2010-01-13
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0051722
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2006-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.