论文标题
Quasi $α$ - 固定在Wasserstein空间中的非专业映射
Quasi $α$-Firmly Nonexpansive Mappings in Wasserstein Spaces
论文作者
论文摘要
本文介绍了$ \ Mathbb r^d $上的Wasserstein空间中的准$α$ -FOLLALE非专业映射的概念，并分析了这些映射的属性。我们证明，对于准$α$ - 固定的非专业映射，满足了一定的二次生长条件，固定点迭代在狭窄的拓扑结构中融合。作为副产品，我们将获得Wasserstein空间中近端算法的已知收敛性。我们将结果应用于首次显示，以最大程度地减少Wasserstein空间上某些功能的总和，在适当的假设下会收敛。
This paper introduces the concept of quasi $α$-firmly nonexpansive mappings in Wasserstein spaces over $\mathbb R^d$ and analyzes properties of these mappings. We prove that for quasi $α$-firmly nonexpansive mappings satisfying a certain quadratic growth condition, the fixed point iterations converge in the narrow topology. As a byproduct, we will get the known convergence of the proximal point algorithm in Wasserstein spaces. We apply our results to show for the first time that cyclic proximal point algorithms for minimizing the sum of certain functionals on Wasserstein spaces converge under appropriate assumptions.
