Abstract

We provide quantitative information in the form of a rate of metastability in the sense of T. Tao and (under a metric regularity assumption) a rate of convergence for an algorithm approximating zeros of differences of maximally monotone operators due to A. Moudafi by using techniques from "proof mining", a subdiscipline of mathematical logic. For the rate of convergence, we provide an abstract and general result on the construction of rates of convergence for quasi-Fejér monotone sequences with metric regularity assumptions, generalizing previous results for Fejér monotone sequences due to U. Kohlenbach, G. López-Acedo and A. Nicolae.

Author information

Contact details are reproduced from the original publication and may be historical.

Keywords

  • Maximally monotone operators
  • Zeros of set-valued operators
  • DC programming
  • Fejér monotonicity
  • proof mining

Mathematics Subject Classification

47H05, 47J25, 03F10, 47H09

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Suggested citation

N. Pischke. “Quantitative Results on Algorithms for Zeros of Differences of Monotone Operators in Hilbert Space.” Journal of Convex Analysis 30 (2023), No. 1, 295–315. https://doi.org/10.68381/jca30016

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Published by Heldermann Verlag, 2023. Rights now held by Banach Press.