标题： 度量空间中的邻近点算法 显示英文标题

标题： The proximal point algorithm in metric spaces

摘要： 近似点算法是一种用于寻找凸函数极小值的著名工具，它从经典的希尔伯特空间框架推广到非正曲率的测地度量空间这一非线性设置中。 我们证明由近似点算法生成的序列弱收敛到一个极小值点，并且还讨论了一个相关问题：梯度流的收敛性。 显示英文摘要

摘要： The proximal point algorithm, which is a well-known tool for finding minima of convex functions, is generalized from the classical Hilbert space framework into a nonlinear setting, namely, geodesic metric spaces of nonpositive curvature. We prove that the sequence generated by the proximal point algorithm weakly converges to a minimizer, and also discuss a related question: convergence of the gradient flow.