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Abstract strongly convergent variants of the proximal point algorithm

Andrei Sipoş ()
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Andrei Sipoş: University of Bucharest

Computational Optimization and Applications, 2022, vol. 83, issue 1, No 11, 349-380

Abstract: 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.

Keywords: Halpern iteration; Proximal point algorithm; CAT(0); Jointly firmly nonexpansive families; Proof mining; Rates of metastability; 90C25; 46N10; 47J25; 47H09; 03F10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10589-022-00397-5

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