On March 19, 2025 at 16:00 EET, Paulo Firmino (University of Lisbon) will give a talk in the Proof Mining Seminar.
Title: Rates of (T-)asymptotic regularity of the generalized Krasnoselskii-Mann-type iteration
Abstract:
In this talk we present the results of a quantitative analysis of work by Zhang, Guo, Wang [4] regarding the generalized Krasnoselskii-Mann-type iteration. We used proof mining methods to compute rates of (T-)asymptotic regularity of the iteration in a uniformly convex normed space, subsequently obtaining corollaries regarding the well-known Krasnoselskii-Mann iteration and other particular cases. We obtain quadratic rates for special choices of the parameter sequences.
This talk reports on recent joint work with Laurențiu Leuștean.
References:
[1] L. Leuștean. Nonexpansive iterations in uniformly convex W-hyperbolic spaces. In B. S. Mordukhovich, I. Shafrir, and A. Zaslavski, editors, Nonlinear Analysis and Optimization I: Nonlinear Analysis, volume 513 of Contemporary Mathematics, pages 193–209. American Mathematical Society, 2010.
[2] L. Leuștean. An application of proof mining to nonlinear iterations. Annals of Pure and Applied Logic, 165:1484–1500, 2014.
[3] C. Kanzow and Y. Shehu. Generalized Krasnoselskii–Mann-type iterations for nonexpansive mappings in Hilbert spaces. Computational Optimization and Applications, 67:595–620, 2017.
[4] Y.-C. Zhang, K. Guo, and T. Wang. Generalized Krasnoselskii-Mann-Type iteration for nonexpansive mappings in Banach spaces. Journal of the Operations Research Society of China, 9:195–206, 2021.
Google Meet link: https://meet.google.com/jpw-hrwe-evu