Attouch-Théra Duality, Generalized Cycles and Gap Vectors

2021/01/14 by Salihah Alwadani, Alwadani, Salihah, Heinz H. Bauschke +3
Mathematics · #(Primary) 47H05 #47A06 #47H09 #47J25 #47N10 #49J53 #49N15 #90C25 (Secondary) #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:47A06 #msc:47H05 #msc:47H09 #msc:47J25 #msc:47N10 #msc:49J53 #msc:49N15 #msc:90C25

paper · pdf · doi:10.48550/arxiv.2101.05857

25 pages

arxiv created 2021/05/03 · arxiv updated 2021/05/04

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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