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Journal of Convex Analysis 30 (2023), No. 1, 295--315
Copyright Heldermann Verlag 2023

Quantitative Results on Algorithms for Zeros of Differences of Monotone Operators in Hilbert Space

Nicholas Pischke
Department of Mathematics, Technische Universitaet Darmstadt, Germany

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.

Keywords: Maximally monotone operators, Zeros of set-valued operators, DC programming, Fejér monotonicity, proof mining.

MSC: 47H05, 47J25, 03F10, 47H09.

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