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Journal of Convex Analysis 28 (2021), No. 1, 011--018
Copyright Heldermann Verlag 2021

Quantitative Results on the Proximal Point Algorithm in Uniformly Convex Banach Spaces

Ulrich Kohlenbach
Department of Mathematics, Technische Universitšt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany

We give rates of strong convergence for the proximal point algorithm PPA computing the unique zero z of operators A in uniformly convex Banach spaces which are uniformly accretive at z. We also get a rate of convergence to some zero of A if A has a modulus of regularity. In the boundedly compact case, we obtain a rate of metastability of PPA in the sense of Tao for arbitrary accretive operators A (satisfying a range condition so that the PPA is well-defined).

Keywords: Accretive operators, proximal point algorithm, uniformly convex Banach spaces, rates of convergence, metastability, proof mining.

MSC: 47H05, 47J25, 03F10.

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