论文标题
Gromov双曲空间中离散的时间梯度流动
Discrete-time gradient flows in Gromov hyperbolic spaces
论文作者
论文摘要
我们研究了Lipschitz凸函数（正确的，地球）Gromov双曲线空间的近端点算法的基本特性。我们表明，来自任意初始点的近端点算法可以找到接近函数最小化器的点。此外，我们为近端（分解）操作员建立收缩估计（类似于树木）。我们的结果可以应用于树木的小扰动。
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 algorithm from an arbitrary initial point can find a point close to a minimizer of the function. Moreover, we establish contraction estimates (akin to trees) for the proximal (resolvent) operator. Our results can be applied to small perturbations of trees.
