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Global Convergence of a Closed-Loop Regularized Newton Method for Solving Monotone Inclusions in Hilbert Spaces

Author

Listed:
  • H. Attouch

    (Université Montpellier II)

  • P. Redont

    (Université Montpellier II)

  • B. F. Svaiter

    (IMPA)

Abstract

We analyze the global convergence properties of some variants of regularized continuous Newton methods for convex optimization and monotone inclusions in Hilbert spaces. The regularization term is of Levenberg–Marquardt type and acts in an open-loop or closed-loop form. In the open-loop case the regularization term may be of bounded variation.

Suggested Citation

  • H. Attouch & P. Redont & B. F. Svaiter, 2013. "Global Convergence of a Closed-Loop Regularized Newton Method for Solving Monotone Inclusions in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 624-650, June.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:3:d:10.1007_s10957-012-0222-3
    DOI: 10.1007/s10957-012-0222-3
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    Cited by:

    1. Samir Adly & Hedy Attouch & Van Nam Vo, 2023. "Convergence of Inertial Dynamics Driven by Sums of Potential and Nonpotential Operators with Implicit Newton-Like Damping," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 290-331, July.
    2. B. Abbas & H. Attouch & Benar F. Svaiter, 2014. "Newton-Like Dynamics and Forward-Backward Methods for Structured Monotone Inclusions in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 331-360, May.

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