SIAM Journal on Optimization, Volume 31, Issue 3, Page 1926-1946, January 2021.
Using the Attouch--Théra duality, we study the cycles, gap vectors, and fixed point sets of compositions of proximal mappings. Sufficient conditions are given for the existence of cycles and gap vectors. A primal-dual framework provides an exact relationship between the cycles and gap vectors. We also introduce the generalized cycle and gap vectors to tackle the case when the classical ones do not exist. Examples are given to illustrate our results.

中文翻译：

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Attouch--Théra 对偶、广义环和间隙向量

SIAM Journal on Optimization，第 31 卷，第 3 期，1926-1946 页，2021 年 1 月。
使用 Attouch--Théra 对偶性，我们研究了近端映射组合的循环、间隙向量和不动点集。给出了循环和间隙向量存在的充分条件。原始对偶框架提供了循环和间隙向量之间的精确关系。我们还引入了广义循环和间隙向量来解决经典循环向量不存在的情况。给出了例子来说明我们的结果。