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Inexact proximal Newton methods in Hilbert spaces

Author

Listed:
  • Bastian Pötzl

    (University of Bayreuth, Chair of Applied Mathematics)

  • Anton Schiela

    (University of Bayreuth, Chair of Applied Mathematics)

  • Patrick Jaap

    (Technische Universität Dresden, Institut für Numerische Mathematik)

Abstract

We consider proximal Newton methods with an inexact computation of update steps. To this end, we introduce two inexactness criteria which characterize sufficient accuracy of these update step and with the aid of these investigate global convergence and local acceleration of our method. The inexactness criteria are designed to be adequate for the Hilbert space framework we find ourselves in while traditional inexactness criteria from smooth Newton or finite dimensional proximal Newton methods appear to be inefficient in this scenario. The performance of the method and its gain in effectiveness in contrast to the exact case are showcased considering a simple model problem in function space.

Suggested Citation

  • Bastian Pötzl & Anton Schiela & Patrick Jaap, 2024. "Inexact proximal Newton methods in Hilbert spaces," Computational Optimization and Applications, Springer, vol. 87(1), pages 1-37, January.
    • Handle: RePEc:spr:coopap:v:87:y:2024:i:1:d:10.1007_s10589-023-00515-x
    DOI: 10.1007/s10589-023-00515-x
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