Inexact proximal Newton methods in Hilbert spaces

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

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.

Details

OriginalspracheEnglisch
Seiten (von - bis)1-37
Seitenumfang37
FachzeitschriftComputational optimization and applications
Jahrgang87 (2024)
Ausgabenummer1
PublikationsstatusVeröffentlicht - 16 Aug. 2023
Peer-Review-StatusJa

Schlagworte

Schlagwörter

  • Inexactness, Non-smooth optimization, Optimization in Hilbert space, Proximal Newton