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math.OC2025
Discrete-time gradient flows for unbounded convex functions on Gromov hyperbolic spaces
Shin-ichi Ohta
In proper, geodesic Gromov hyperbolic spaces, we investigate discrete-time gradient flows via the proximal point algorithm for unbounded Lipschitz convex functions. Assuming that t…
math.OC2023
How does the contraction property fail for convex functions on normed spaces?
Shin-ichi Ohta
On Euclidean and Hilbert spaces, Riemannian manifolds, and CAT-spaces, gradient flows of convex functions are known to satisfy the contraction property, which plays a fundamen…
math.OC2022
Discrete-time gradient flows in Gromov hyperbolic spaces
Shin-ichi Ohta
We investigate fundamental properties of the proximal point algorithm for Lipschitz convex functions on (proper, geodesic) Gromov hyperbolic spaces. We show that the proximal point…