Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 31, Issue 3, Pages 1926-1946Publisher
SIAM PUBLICATIONS
DOI: 10.1137/21M1392085
Keywords
Key words; Attouch--The'; ra; duality; circular right shift operator; convex function; displacement mapping; generalized cycle; generalized gap vector; proximal cycle; proximal mapping
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Funding
- Natural Sciences and Engineering Research Council of Canada
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Using the Attouch-The'\ra duality, cycles, gap vectors, and fixed point sets of compositions of proximal mappings are studied, with sufficient conditions given for the existence of cycles and gap vectors. A primal-dual framework establishes an exact relationship between the cycles and gap vectors, and generalized cycle and gap vectors are introduced for cases where classical ones do not exist. Examples are provided to illustrate the results.
Using the Attouch--The'\ra 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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