Abstract

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).

Author information

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Keywords

  • Accretive operators
  • proximal point algorithm
  • uniformly convex Banach spaces
  • rates of convergence
  • metastability
  • proof mining

Mathematics Subject Classification

47H05, 47J25, 03F10

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Suggested citation

U. Kohlenbach. “Quantitative Results on the Proximal Point Algorithm in Uniformly Convex Banach Spaces.” Journal of Convex Analysis 28 (2021), No. 1, 11–18. https://doi.org/10.68381/jca28002

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press LLC.