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

Title: Computing the resolvent of the sum of operators with application to best approximation problems
Creator: Dao, Minh; Phan, Hung
Date: 2019
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/185610
Identifier: vital:16698
Identifier: https://doi.org/10.1007/s11590-019-01432-x
Identifier: ISBN:1862-4472
Abstract: We propose a flexible approach for computing the resolvent of the sum of weakly monotone operators in real Hilbert spaces. This relies on splitting methods where strong convergence is guaranteed. We also prove linear convergence under Lipschitz continuity assumption. The approach is then applied to computing the proximity operator of the sum of weakly convex functions, and particularly to finding the best approximation to the intersection of convex sets.
Publisher: Berlin/Heidelberg: Springer Berlin Heidelberg
Relation: Optimization letters Vol. 14, no. 5 (2019), p. 1193-1205
Rights: All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
Subject: Computational Intelligence; Mathematics; Mathematics and Statistics; Numerical and Computational Physics; Operations Research/Decision Theory; Optimization; Original Paper; Simulation; 4901 Applied mathematics
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