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A comparison of reduced and unreduced KKT systems arising from interior point methods

Author

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  • Benedetta Morini

    (Università degli Studi di Firenze)

  • Valeria Simoncini

    (Dipartimento di Matematica, Università di Bologna)

  • Mattia Tani

    (Università di Pavia)

Abstract

We address the iterative solution of KKT systems arising in the solution of convex quadratic programming problems. Two strictly related and well established formulations for such systems are studied with particular emphasis on the effect of preconditioning strategies on their relation. Constraint and augmented preconditioners are considered, and the choice of the augmentation matrix is discussed. A theoretical and experimental analysis is conducted to assess which of the two formulations should be preferred for solving large-scale problems.

Suggested Citation

  • Benedetta Morini & Valeria Simoncini & Mattia Tani, 2017. "A comparison of reduced and unreduced KKT systems arising from interior point methods," Computational Optimization and Applications, Springer, vol. 68(1), pages 1-27, September.
    • Handle: RePEc:spr:coopap:v:68:y:2017:i:1:d:10.1007_s10589-017-9907-8
    DOI: 10.1007/s10589-017-9907-8
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    References listed on IDEAS

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    1. S. Bellavia, 1998. "Inexact Interior-Point Method," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 109-121, January.
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    Cited by:

    1. Benedetta Morini & Valeria Simoncini, 2017. "Stability and Accuracy of Inexact Interior Point Methods for Convex Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 450-477, November.
    2. J. Gondzio & F. N. C. Sobral, 2019. "Quasi-Newton approaches to interior point methods for quadratic problems," Computational Optimization and Applications, Springer, vol. 74(1), pages 93-120, September.
    3. Stefano Cipolla & Jacek Gondzio, 2023. "Proximal Stabilized Interior Point Methods and Low-Frequency-Update Preconditioning Techniques," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1061-1103, June.
    4. David Ek & Anders Forsgren, 2023. "A structured modified Newton approach for solving systems of nonlinear equations arising in interior-point methods for quadratic programming," Computational Optimization and Applications, Springer, vol. 86(1), pages 1-48, September.

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