On the asymptotic behaviour of the Aragon Artacho-Campoy algorithm

2018/05/28 by Salihah Alwadani, Heinz H. Bauschke, Alwadani, Salihah +5
Computer Science · Mathematics · #49M27 #65K05 #65K10 #90C25 #Advanced Optimization Algorithms Research #FOS: Mathematics #Mathematical Inequalities and Applications #Optimization and Control (math.OC) #Optimization and Variational Analysis #Primary 47H05 #Secondary 47H09 #math.OC #msc:47H05 #msc:47H09 #msc:49M27 #msc:65K05 #msc:65K10 #msc:90C25

paper · pdf · doi:10.48550/arxiv.1805.11165

arxiv created 2018/05/28 · openalex publication_date 2018/05/28 · arxiv updated 2018/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Aragón 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.

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