Inexact proximal Newton methods in Hilbert spaces

Bastian Pötzl (), Anton Schiela () and Patrick Jaap ()
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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

Computational Optimization and Applications, 2024, vol. 87, issue 1, No 1, 37 pages

Abstract: 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.

Keywords: Non-smooth optimization; Optimization in Hilbert space; Proximal Newton; Inexactness; 49M15; 49M37; 65K10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-023-00515-x

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