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
pischkenicholas@gmail.com
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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