2021/09/14 by Briceño-Arias, Luis, Roldán, Fernando
#47H05 #47H10 #49M29 #65K05 #65K15 #90C25 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2109.06771
In this paper we provide the resolvent computation of the parallel composition of a maximally monotone operator by a linear operator under mild assumptions. Connections with a modification of the warped resolvent are provided. In the context of convex optimization, we obtain the proximity operator of the infimal postcomposition of a convex function by a linear operator and we extend full range conditions on the linear operator to mild qualification conditions. We also introduce a generalization of the proximity operator involving a general linear bounded operator leading to a generalization of Moreau's decomposition for composite convex optimization.