哈达玛流形上的近端梯度法收敛性分析
Analysis of Convergence of Proximal Gradient Method on Hadamard Manifold
摘要: 本文在哈达玛流形上提出了近端梯度算法，并给出了收敛性分析。具体地说，我们将非凸非光滑问题的近端梯度法从欧氏空间推广到哈达玛流形上。在黎曼流形上存在着非线性的困难，我们根据哈达玛流形的特殊结构，给出了理论证明。
Abstract: In this paper, a proximal gradient algorithm for Hadamard manifolds is presented and its conver-gence is analyzed. Specifically, we extend the proximal gradient method for Nonconvex nonsmooth problems from Euclidan space to Hadamard manifolds. The difficulty of nonlinearity on Bernhard Riemann manifolds is proved theoretically according to the special structure of Hadamard mani-folds. In this paper, a proximal gradient algorithm for Hadamard manifolds is presented and its convergence is analyzed. Specifically, we extend the proximal gradient method for nonconvex nonsmooth problems from Euclidean space to Hadamard manifolds. The difficulty of nonlinearity on Bernhard Riemann manifolds is proved theoretically according to the special structure of Hadamard manifolds.
文章引用：宋乐乐. 哈达玛流形上的近端梯度法收敛性分析[J]. 理论数学, 2021, 11(5): 701-708. https://doi.org/10.12677/PM.2021.115085

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