Quantitative results on a Halpern-type proximal point algorithm
Copyright policy )Quantitative results on a Halpern-type proximal point algorithm
We apply proof mining methods to analyse a result of Boikanyo and Moro��anu on the strong convergence of a Halpern-type proximal point algorithm. As a consequence, we obtain quantitative versions of this result, providing uniform effective rates of asymptotic regularity and metastability.
This is a preprint of an article published in Computational Optimization and Applications. The final authenticated version is available online at: https://doi.org/10.1007/s10589-021-00263-w
- University of Bucharest Romania
- TU Darmstadt Germany
- Department of Computer Sciences Austria
- Department of Computer Science Spain
- Department of Mathematics
Halpern iteration, rates of convergence, rates of metastability, Mathematics - Logic, Functionals in proof theory, proximal point algorithm, maximally monotone operators, 47H05, 47H09, 47J25, 03F10, Iterative procedures involving nonlinear operators, proof mining, Optimization and Control (math.OC), FOS: Mathematics, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., Logic (math.LO), Monotone operators and generalizations, Mathematics - Optimization and Control
Halpern iteration, rates of convergence, rates of metastability, Mathematics - Logic, Functionals in proof theory, proximal point algorithm, maximally monotone operators, 47H05, 47H09, 47J25, 03F10, Iterative procedures involving nonlinear operators, proof mining, Optimization and Control (math.OC), FOS: Mathematics, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., Logic (math.LO), Monotone operators and generalizations, Mathematics - Optimization and Control
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