Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces

Dello Schiavo L, Maas J, Pedrotti F. 2024. Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces. Transactions of the American Mathematical Society. 377(6), 3779–3804.

Download (ext.)

Journal Article | Published | English

Scopus indexed
Department
Abstract
This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations. To obtain quantitative estimates on the speed of convergence, we consider variations on the classical Kurdyka–Łojasiewicz inequality for a large class of parameter functions. Our assumptions are given in terms of the initial data, without any reference to an equilibrium point. The main results are convergence statements for gradient flow curves and proximal point sequences to a global minimiser, together with sharp quantitative estimates on the speed of convergence. These convergence results apply in the general setting of lower semicontinuous functionals on complete metric spaces, generalising recent results for smooth functionals on Rn. While the non-smooth setting covers very general spaces, it is also useful for (non)-smooth functionals on Rn. .
Publishing Year
Date Published
2024-06-01
Journal Title
Transactions of the American Mathematical Society
Publisher
American Mathematical Society
Acknowledgement
The authors gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 716117). This research was funded in part by the Austrian Science Fund (FWF) project 10.55776/ESP208. This research was funded in part by the Austrian Science Fund (FWF) project 10.55776/F65
Volume
377
Issue
6
Page
3779-3804
ISSN
eISSN
IST-REx-ID

Cite this

Dello Schiavo L, Maas J, Pedrotti F. Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces. Transactions of the American Mathematical Society. 2024;377(6):3779-3804. doi:10.1090/tran/9156
Dello Schiavo, L., Maas, J., & Pedrotti, F. (2024). Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/9156
Dello Schiavo, Lorenzo, Jan Maas, and Francesco Pedrotti. “Local Conditions for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric Spaces.” Transactions of the American Mathematical Society. American Mathematical Society, 2024. https://doi.org/10.1090/tran/9156.
L. Dello Schiavo, J. Maas, and F. Pedrotti, “Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces,” Transactions of the American Mathematical Society, vol. 377, no. 6. American Mathematical Society, pp. 3779–3804, 2024.
Dello Schiavo L, Maas J, Pedrotti F. 2024. Local conditions for global convergence of gradient flows and proximal point sequences in metric spaces. Transactions of the American Mathematical Society. 377(6), 3779–3804.
Dello Schiavo, Lorenzo, et al. “Local Conditions for Global Convergence of Gradient Flows and Proximal Point Sequences in Metric Spaces.” Transactions of the American Mathematical Society, vol. 377, no. 6, American Mathematical Society, 2024, pp. 3779–804, doi:10.1090/tran/9156.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]

Link(s) to Main File(s)
Access Level
OA Open Access
Material in ISTA:
Dissertation containing ISTA record

Export

Marked Publications

Open Data ISTA Research Explorer

Sources

arXiv 2304.05239

Search this title in

Google Scholar