论文标题
非专用映射的组成的固定点：有限的许多线性反射器
Fixed points of compositions of nonexpansive mappings: finitely many linear reflectors
论文作者
论文摘要
非专用映射在现代优化和单调操作员理论中起着核心作用，因为它们的固定点可以描述优化或关键点问题的解决方案。众所周知，当映射足够“不错”时，组合物的固定点集与单个固定点集的相交相吻合。在本文中，我们探讨了线性反射器组成的情况。我们提供积极的结果，上限和极限示例。我们还讨论了欧几里得平面中的经典反射器。
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently "nice", then the fixed point set of the composition coincides with the intersection of the individual fixed point sets. In this paper, we explore the situation for compositions of linear reflectors. We provide positive results, upper bounds, and limiting examples. We also discuss classical reflectors in the Euclidean plane.
