Discrete-time gradient flows for unbounded convex functions on Gromov hyperbolic spaces

Ohta, Shin-Ichi

Communications in Contemporary Mathematics, 2025, 2650003

アクセス数:7件（2026-02-16 01:32 集計）

固定URL: https://hdl.handle.net/11094/103619

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タイトル
Discrete-time gradient flows for unbounded convex functions on Gromov hyperbolic spaces
著者
NRID
1000000372558 1000000372558
ORCID
0000-0001-9967-6737 0000-0001-9967-6737
researchmap permalink
7000008399 7000008399
Scopus Author ID
35300531200 35300531200
著者名
Ohta, Shin-Ichi
キーワード等
convex function
gradient flow
Gromov hyperbolic space
内容
Electronic version of an article published as Communications in Contemporary Mathematics, 2025, https://doi.org/10.1142/S0219199726500033
抄録
In proper, geodesic Gromov hyperbolic spaces, we investigate discrete-time gradient flows via the proximal point algorithm for unbounded Lipschitz convex functions. Assuming that the target convex function has negative asymptotic slope along some ray (thus unbounded below), we first prove the uniqueness of such a negative direction in the boundary at infinity. Then, we show that the discrete-time gradient flow from an arbitrary initial point diverges to that unique direction of negative asymptotic slope. This is inspired by and generalizes results of Karlsson–Margulis and Hirai–Sakabe on nonpositively curved spaces and a result of Karlsson concerning semi-contractions on Gromov hyperbolic spaces. We also give an estimate of the rate of convergence based on a contraction property for the proximal (resolvent) operator established in our previous work.
出版者
World Scientific
収録物名
Communications in Contemporary Mathematics
ページ
2650003
刊行年月
2025-12-11
言語
英語
ハンドルURL
https://hdl.handle.net/11094/103619
PISSN
02191997
eISSN
17936683
関連情報 (isVersionOf)
DOI (出版社版)
https://doi.org/10.1142/S0219199726500033
アクセス権
embargoed access
権利情報
The full-text file will be made open to the public on 11 December 2026 in accordance with the publisher's policy.
© 2026 World Scientific Publishing Company.
出版タイプ
Accepted Manuscript
カテゴリ
学術雑誌論文 Journal Article