Second order semi-smooth Proximal Newton methods in Hilbert spaces

Bastian Pötzl (), Anton Schiela () and Patrick Jaap ()
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Bastian Pötzl: University of Bayreuth
Anton Schiela: University of Bayreuth
Patrick Jaap: Technische Universität Dresden

Computational Optimization and Applications, 2022, vol. 82, issue 2, No 6, 465-498

Abstract: 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.

Keywords: Non-smooth Optimization; Optimization in Hilbert space; Proximal Newton; 49M15; 49M37 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-022-00369-9

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