On October 17, 2024 at 14:00 EEST, Horațiu Cheval (University of Bucharest) will give a talk in the Logic Seminar.
Title: Proof mining and applications to optimization and nonlinear analysis
Abstract:
We present the main results from [1], obtained as part of the program of proof mining, consisting of quantitative information on the asymptotic behavior of iterations from optimization and nonlinear analysis. We begin with a brief introduction to proof mining, after which we present results concerning the Tikhonov-Mann and modified Halpern iterations for finding fixed points of nonexpansive mappings in a very general nonlinear setting, where the main quantitative content we get takes the form of uniform rates of asymptotic regularity. This then generalizes to iterations for approximating common fixed points of families of nonexpansive mappings, for which we again compute rates of asymptotic regularity, as well as rates of metastability. Finally, we obtain linear rates of asymptotic regularity for a variety of iterations encountered in the optimization literature.
References:
[1] H. Cheval. Proof mining and applications to optimization and nonlinear analysis. PhD Thesis, submitted, 2024.
The talk will take place physically at FMI (Academiei 14), Hall 214 “Google”.