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Clustering-based preconditioning for stochastic programs

Author

Listed:
  • Yankai Cao

    (Purdue University)

  • Carl D. Laird

    (Purdue University)

  • Victor M. Zavala

    (University of Wisconsin-Madison)

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.

Suggested Citation

  • Yankai Cao & Carl D. Laird & Victor M. Zavala, 2016. "Clustering-based preconditioning for stochastic programs," Computational Optimization and Applications, Springer, vol. 64(2), pages 379-406, June.
    • Handle: RePEc:spr:coopap:v:64:y:2016:i:2:d:10.1007_s10589-015-9813-x
    DOI: 10.1007/s10589-015-9813-x
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    References listed on IDEAS

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    Cited by:

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    2. Sungho Shin & Ophelia S Venturelli & Victor M Zavala, 2019. "Scalable nonlinear programming framework for parameter estimation in dynamic biological system models," PLOS Computational Biology, Public Library of Science, vol. 15(3), pages 1-29, March.

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