Attouch-Th\'era Duality, Generalized Cycles and Gap Vectors
Optimization and Control
2021-05-04 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2101.05857,
title = {Attouch-Th\'era Duality, Generalized Cycles and Gap Vectors},
author = {Salihah Alwadani and Heinz H. Bauschke and Xianfu Wang},
journal= {arXiv preprint arXiv:2101.05857},
year = {2021}
}
Comments
25 pages