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Clustering-based preconditioning for stochastic programs
We present a clustering-based preconditioning strategy for KKT systems arising in stochastic programming within an interior-point framework. The key idea is to perform adaptive clustering of scenarios (inside-the-solver) based on their influence on the problem at hand. This approach thus contrasts w...
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Published in: | Computational optimization and applications 2016-06, Vol.64 (2), p.379-406 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | We present a clustering-based preconditioning strategy for KKT systems arising in stochastic programming within an interior-point framework. The key idea is to perform adaptive clustering of scenarios (inside-the-solver) based on their influence on the problem at hand. This approach thus contrasts with existing (outside-the-solver) approaches that cluster scenarios based on problem data alone. We derive spectral and error properties for the preconditioner and demonstrate that scenario compression rates of up to 94Â % can be obtained, leading to dramatic computational savings. In addition, we demonstrate that the proposed preconditioner can avoid scalability issues of Schur decomposition in problems with large first-stage dimensionality. |
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ISSN: | 0926-6003 1573-2894 |
DOI: | 10.1007/s10589-015-9813-x |