Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/305787 
Erscheinungsjahr: 
2023
Quellenangabe: 
[Journal:] Computational Optimization and Applications [ISSN:] 1573-2894 [Volume:] 87 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2023 [Pages:] 1-37
Verlag: 
Springer US, New York, NY
Zusammenfassung: 
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.
Schlagwörter: 
Non-smooth optimization
Optimization in Hilbert space
Proximal Newton
Inexactness
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