发表机构
Università di Genova（热那亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究瓦瑟斯坦空间中不同凸性概念下近端算子的稳定性，通过对各种泛函凸性进行探讨，特别关注其非扩张性，以深入理解该算子在瓦瑟斯坦空间中的收缩性质。
AI 中文摘要
近端算子是变分分析和优化中的基本工具。在希尔伯特空间中，给定一个适当的、下半连续凸泛函，其近端算子是非扩张的，即 1 - 利普希茨连续。在瓦瑟斯坦空间中，Carlen、Craig、Adve 和 Mészáros 等人从不同角度研究了该算子的收缩性质，但尚未完全理解。本文研究了在瓦瑟斯坦空间中可考虑的各种泛函凸性概念下近端映射的稳定性性质，特别关注非扩张性。
英文摘要
The proximal operator is a fundamental tool in variational analysis and optimization. In the setting of a Hilbert space, given a proper, lower semicontinuous convex functional, its proximal operator is non-expansive, that is, 1-Lipschitz continuous. In the Wasserstein setting, the contraction properties of this operator have been investigated from different perspectives by Carlen and Craig and by Adve and Mészáros, among others, and are not completely understood. In this paper, we study the stability properties of proximal maps, with a particular focus on non-expansivity, under various notions of convexity of the functional that can be considered in the Wasserstein space.
