Computing the resolvent of the sum of operators with application to best\n approximation problems

2018/09/11 by Minh N. Dao, Dao, Minh N., Hung M. Phan +1 · 1 citation
Computer Science · Mathematics · #49M27 #65K05 #65K10 #FOS: Mathematics #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Optimization and Variational Analysis #Primary: 47H05 #Secondary: 47H10

paper · pdf · doi:10.48550/arxiv.1809.03921

openalex publication_date 2018/09/11 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

Abstract

We propose a flexible approach for computing the resolvent of the sum of\nweakly monotone operators in real Hilbert spaces. This relies on splitting\nmethods where strong convergence is guaranteed. We also prove linear\nconvergence under Lipschitz continuity assumption. The approach is then applied\nto computing the proximity operator of the sum of weakly convex functions, and\nparticularly to finding the best approximation to the intersection of convex\nsets.\n

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