On the asymptotic behaviour of the Aragon Artacho-Campoy algorithm

Salihah Alwadani, Heinz H. Bauschke, Walaa M. Moursi, X. Wang

Published 2018-05-28Version 1

Arag\'on Artacho and Campoy recently proposed a new method for computing the projection onto the intersection of two closed convex sets in Hilbert space; moreover, they proposed in 2018 a generalization from normal cone operators to maximally monotone operators. In this paper, we complete this analysis by demonstrating that the underlying curve converges to the nearest zero of the sum of the two operators. We also provide a new interpretation of the underlying operators in terms of the resolvent and the proximal average.