Attouch--Théra Duality, Generalized Cycles, and Gap Vectors
利用Attouch-Théra对偶研究近端映射复合的循环、间隙向量和不动点集，给出存在性条件，并引入广义概念处理经典情形不存在的情况。
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.