Title data
Pötzl, Bastian ; Schiela, Anton ; Jaap, Patrick:
Second order semismooth proximal Newton methods in Hilbert spaces.
Bayreuth
,
2021
.  28 p.
Project information
Project title: 



Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract in another language
We develop a globalized Proximal Newton method for composite and possibly nonconvex 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 semismoothness 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.