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Second order semi-smooth Proximal Newton methods in Hilbert spaces

Author

Listed:
  • Bastian Pötzl

    (University of Bayreuth)

  • Anton Schiela

    (University of Bayreuth)

  • Patrick Jaap

    (Technische Universität Dresden)

Abstract

We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose less restrictive assumptions on the composite objective functional considering differentiability and convexity than in existing theory. As far as differentiability of the smooth part of the objective function is concerned, we introduce the notion of second order semi-smoothness and discuss why it constitutes an adequate framework for our Proximal Newton method. However, both global convergence as well as local acceleration still pertain to hold in our scenario. Eventually, the convergence properties of our algorithm are displayed by solving a toy model problem in function space.

Suggested Citation

  • Bastian Pötzl & Anton Schiela & Patrick Jaap, 2022. "Second order semi-smooth Proximal Newton methods in Hilbert spaces," Computational Optimization and Applications, Springer, vol. 82(2), pages 465-498, June.
    • Handle: RePEc:spr:coopap:v:82:y:2022:i:2:d:10.1007_s10589-022-00369-9
    DOI: 10.1007/s10589-022-00369-9
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    References listed on IDEAS

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    1. Kimon Fountoulakis & Rachael Tappenden, 2018. "A flexible coordinate descent method," Computational Optimization and Applications, Springer, vol. 70(2), pages 351-394, June.
    2. Lorenzo Stella & Andreas Themelis & Panagiotis Patrinos, 2017. "Forward–backward quasi-Newton methods for nonsmooth optimization problems," Computational Optimization and Applications, Springer, vol. 67(3), pages 443-487, July.
    3. Ching-pei Lee & Stephen J. Wright, 2019. "Inexact Successive quadratic approximation for regularized optimization," Computational Optimization and Applications, Springer, vol. 72(3), pages 641-674, April.
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