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Stability and Accuracy of Inexact Interior Point Methods for Convex Quadratic Programming

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  • Benedetta Morini

    (Università degli Studi di Firenze)

  • Valeria Simoncini

    (Università di Bologna
    IMATI-CNR)

Abstract

We consider primal–dual interior point methods where the linear system arising at each iteration is formulated in the reduced (augmented) form and solved approximately. Focusing on the iterates close to a solution, we analyze the accuracy of the so-called inexact step, i.e., the step that solves the unreduced system, when combining the effects of both different levels of accuracy in the inexact computation and different processes for retrieving the step after block elimination. Our analysis is general and includes as special cases sources of inexactness due either to roundoff and computational errors or to the iterative solution of the augmented system using typical procedures. In the roundoff case, we recover and extend some known results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:175:y:2017:i:2:d:10.1007_s10957-017-1170-8
    DOI: 10.1007/s10957-017-1170-8
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    References listed on IDEAS

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    1. Paul Armand & Joël Benoist & Jean-Pierre Dussault, 2012. "Local path-following property of inexact interior methods in nonlinear programming," Computational Optimization and Applications, Springer, vol. 52(1), pages 209-238, May.
    2. 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.
    3. C. Durazzi & V. Ruggiero, 2004. "Global Convergence of the Newton Interior-Point Method for Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 199-208, January.
    4. S. Bellavia, 1998. "Inexact Interior-Point Method," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 109-121, January.
    5. G. Al-Jeiroudi & J. Gondzio, 2009. "Convergence Analysis of the Inexact Infeasible Interior-Point Method for Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 231-247, May.
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    Cited by:

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    2. David Ek & Anders Forsgren, 2021. "Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization," Computational Optimization and Applications, Springer, vol. 79(1), pages 155-191, May.

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