Abstract
We prove an abstract form of the strong convergence of the Halpern-type and Tikhonov-type proximal point algorithms in CAT(0) spaces. In addition, we derive uniform and computable rates of metastability (in the sense of Tao) for these iterations using proof mining techniques.
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Acknowledgements
I would like to thank Ulrich Kohlenbach and Laurenţiu Leuştean for their suggestions. This work has been supported by a grant of the Romanian Ministry of Research, Innovation and Digitization, CNCS/CCCDI – UEFISCDI, Project Number PN-III-P1-1.1-PD-2019-0396, within PNCDI III.
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Sipoş, A. Abstract strongly convergent variants of the proximal point algorithm. Comput Optim Appl 83, 349–380 (2022). https://doi.org/10.1007/s10589-022-00397-5
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DOI: https://doi.org/10.1007/s10589-022-00397-5
Keywords
- Halpern iteration
- Proximal point algorithm
- CAT(0)
- Jointly firmly nonexpansive families
- Proof mining
- Rates of metastability