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General-purpose preconditioning for regularized interior point methods

Author

Listed:
  • Jacek Gondzio

    (University of Edinburgh)

  • Spyridon Pougkakiotis

    (Yale University)

  • John W. Pearson

    (University of Edinburgh)

Abstract

In this paper we present general-purpose preconditioners for regularized augmented systems, and their corresponding normal equations, arising from optimization problems. We discuss positive definite preconditioners, suitable for CG and MINRES. We consider “sparsifications" which avoid situations in which eigenvalues of the preconditioned matrix may become complex. Special attention is given to systems arising from the application of regularized interior point methods to linear or nonlinear convex programming problems.

Suggested Citation

  • Jacek Gondzio & Spyridon Pougkakiotis & John W. Pearson, 2022. "General-purpose preconditioning for regularized interior point methods," Computational Optimization and Applications, Springer, vol. 83(3), pages 727-757, December.
    • Handle: RePEc:spr:coopap:v:83:y:2022:i:3:d:10.1007_s10589-022-00424-5
    DOI: 10.1007/s10589-022-00424-5
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    References listed on IDEAS

    as
    1. Spyridon Pougkakiotis & Jacek Gondzio, 2019. "Dynamic Non-diagonal Regularization in Interior Point Methods for Linear and Convex Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 905-945, June.
    2. Luca Bergamaschi & Jacek Gondzio & Manolo Venturin & Giovanni Zilli, 2007. "Inexact constraint preconditioners for linear systems arising in interior point methods," Computational Optimization and Applications, Springer, vol. 36(2), pages 137-147, April.
    3. Spyridon Pougkakiotis & Jacek Gondzio, 2022. "An Interior Point-Proximal Method of Multipliers for Linear Positive Semi-Definite Programming," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 97-129, January.
    4. Maros, Istvan & Meszaros, Csaba, 1998. "The role of the augmented system in interior point methods," European Journal of Operational Research, Elsevier, vol. 107(3), pages 720-736, June.
    5. Spyridon Pougkakiotis & Jacek Gondzio, 2021. "An interior point-proximal method of multipliers for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 78(2), pages 307-351, March.
    6. Paul Armand & Riadh Omheni, 2017. "A Mixed Logarithmic Barrier-Augmented Lagrangian Method for Nonlinear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 523-547, May.
    7. Stefania Bellavia & Valentina De Simone & Daniela di Serafino & Benedetta Morini, 2016. "On the update of constraint preconditioners for regularized KKT systems," Computational Optimization and Applications, Springer, vol. 65(2), pages 339-360, November.
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