Attouch--Théra Duality, Generalized Cycles, and Gap Vectors
Abstract
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.
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DOI:10.1137/sjope8.31.3
Issue’s Table of Contents© 2021, Society for Industrial and Applied Mathematics.
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Society for Industrial and Applied Mathematics
United States
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Published: 01 January 2021
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