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Quasi-Newton methods in infinite-dimensional spaces and application to matrix equations

Author

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  • Boubakeur Benahmed
  • Hocine Mokhtar-Kharroubi
  • Bruno Malafosse
  • Adnan Yassine

Abstract

In the first part of this paper, we give a survey on convergence rates analysis of quasi-Newton methods in infinite Hilbert spaces for nonlinear equations. Then, in the second part we apply quasi-Newton methods in their Hilbert formulation to solve matrix equations. So, we prove, under natural assumptions, that quasi-Newton methods converge locally and superlinearly; the global convergence is also studied. For numerical calculations, we propose new formulations of these methods based on the matrix representation of the dyadic operator and the vectorization of matrices. Finally, we apply our results to algebraic Riccati equations. Copyright Springer Science+Business Media, LLC. 2011

Suggested Citation

  • Boubakeur Benahmed & Hocine Mokhtar-Kharroubi & Bruno Malafosse & Adnan Yassine, 2011. "Quasi-Newton methods in infinite-dimensional spaces and application to matrix equations," Journal of Global Optimization, Springer, vol. 49(3), pages 365-379, March.
    • Handle: RePEc:spr:jglopt:v:49:y:2011:i:3:p:365-379
    DOI: 10.1007/s10898-010-9564-2
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    Cited by:

    1. F. Aragón Artacho & A. Belyakov & A. Dontchev & M. López, 2014. "Local convergence of quasi-Newton methods under metric regularity," Computational Optimization and Applications, Springer, vol. 58(1), pages 225-247, May.

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