Attouch-Th\'era Duality, Generalized Cycles and Gap Vectors

Autor:	Alwadani, Salihah, Bauschke, Heinz H., Wang, Xianfu
Rok vydání:	2021
Předmět:	Mathematics - Optimization and Control (Primary) 47H05 49J53 47H09 47N10 49N15 47A06 47J25 90C25 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Using the Attouch-Th\'era 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. Comment: 25 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2101.05857 Zobrazit plný text záznamu View this record from Arxiv