Clustering-based preconditioning for stochastic programs

Yankai Cao (), Carl D. Laird () and Victor M. Zavala ()
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Yankai Cao: Purdue University
Carl D. Laird: Purdue University
Victor M. Zavala: University of Wisconsin-Madison

Computational Optimization and Applications, 2016, vol. 64, issue 2, No 3, 379-406

Abstract: Abstract 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 94 % 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.

Keywords: Preconditioning; Interior-point; Stochastic; Large-scale; Clustering (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-015-9813-x

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