Tootfinder

Halpern Acceleration of the Inexact Proximal Point Method of Rockafellar
Liwei Zhang, Fanli Zhuang, Ning Zhang
https://arxiv.org/abs/2511.10372 https://arxiv.org/pdf/2511.10372 https://arxiv.org/html/2511.10372
arXiv:2511.10372v1 Announce Type: new
Abstract: This paper investigates a Halpern acceleration of the inexact proximal point method for solving maximal monotone inclusion problems in Hilbert spaces. The proposed Halpern inexact proximal point method (HiPPM) is shown to be globally convergent, and a unified framework is developed to analyze its worst-case convergence rate. Under mild summability conditions on the inexactness tolerances, HiPPM achieves an $\mathcal{O}(1/k^{2})$ rate in terms of the squared fixed-point residual. Furthermore, under additional mild condition, the method retains a fast linear convergence rate. Building upon this framework, we further extend the acceleration technique to constrained convex optimization through the augmented Lagrangian formulation. In analogy to Rockafellar's classical results, the resulting accelerated inexact augmented Lagrangian method inherits the convergence rate and complexity guarantees of HiPPM. The analysis thus provides a unified theoretical foundation for accelerated inexact proximal algorithms and their augmented Lagrangian extensions.
toXiv_bot_toot

Das Rechtsgutachten, welches unser lieber OB Hilbert in Auftrag gegeben hat, weil ihm die Einschätzung des eigenen Rechtsamts zum DVB Bürgerbegehren nicht gepasst hat, hat fast 19.000 € gekostet! 😱
Das sind ca. 1.250 € pro Seite! 😱
https://archive.is/n55b5

Wir haben in der #Mathe-Fakultät einen neuen Raum der für "Verpflegung" vorgesehen ist. Wie soll er heißen?
Schnitzelraum
Hilbertraum
Eigenraum
3-Eck
Gerüchteküche
Keine Badeanstalt
Konvergenzraum
Integral
La Place
Zusammen Setzen (ZuSe)
Uncommon Room
Poin Carré
Leibniz
Komplement
Mathe-Oase
Delta-Raum
Schottisches Café
φ-Bert Raum
Der Nullraum/ Kernel room
Tofu-Raum
!Café
Fakultätscafé
Linsenraum
?