Geodesic
Quantitative Results on the Proximal Point Algorithm in Uniformly Convex Banach Spaces
Journal of convex analysis, Tome 28 (2021) no. 1, pp. 11-18
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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).
Classification : 47H05, 47J25, 03F10
Mots-clés : Accretive operators, proximal point algorithm, uniformly convex Banach spaces, rates of convergence, metastability, proof mining 
@article{JCA_2021_28_1_JCA_2021_28_1_a1,
     author = {U. Kohlenbach},
     title = {Quantitative {Results} on the {Proximal} {Point} {Algorithm} in {Uniformly} {Convex} {Banach} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {11--18},
     year = {2021},
     volume = {28},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2021_28_1_JCA_2021_28_1_a1/}
}
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U. Kohlenbach. Quantitative Results on the Proximal Point Algorithm in Uniformly Convex Banach Spaces. Journal of convex analysis, Tome 28 (2021) no. 1, pp. 11-18. http://geodesic.mathdoc.fr/item/JCA_2021_28_1_JCA_2021_28_1_a1/