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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
kohlenbach@mathematik.tu-darmstadt.de



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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