Quantitative results on algorithms for zeros of differences of monotone operators in Hilbert space

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-Fej\'er monotone sequences with metric regularity assumptions, generalizing previous results for Fej\'er monotone sequences due to U. Kohlenbach, G. L\'opez-Acedo and A. Nicolae.