On January 15, 2025 at 16:00 EET, Pedro Pinto (TU Darmstadt) will give a talk in the Proof Mining Seminar.
Title: On the Halpern method with adaptive anchoring parameters
Abstract:
In this talk, I will present a proof mining analysis of a recent result by He, Xu, Dong, and Mei [1], which introduces an accelerated version of the Halpern iteration with adaptively chosen anchoring parameters. Our quantitative study extends the convergence result from its original framework in Hilbert spaces to the broader nonlinear setting of Hadamard spaces. This generalization is achieved through a combination of certain optimizations and the elimination of weak compactness arguments, enabling the extraction of simple rates of metastability and fast rates of asymptotic regularity.
This talk reports on recent joint work with Nicholas Pischke.
References:
[1] S. He, H.-K. Xu, Q.-L. Dong, and N. Mei. Convergence analysis of the Halpern iteration with adaptive anchoring parameters. Mathematics of Computation, 93:327–345, 2024.
[2] P. Pinto, and N. Pischke. On the Halpern method with adaptive anchoring parameters. Oberwolfach Preprint OWP-2024-11, 2024.
[3] U. Kohlenbach. Some logical metatheorems with applications in functional analysis. Transactions of the American Mathematical Society, 357(1):89–128, 2005.
[4] U. Kohlenbach. Applied Proof Theory: Proof Interpretations and their Use in Mathematics. Springer Monographs in Mathematics. Springer-Verlag Berlin Heidelberg, 2008.
[5] F. Ferreira, L. Leuștean, and P. Pinto. On the removal of weak compactness arguments in proof mining. Advances in Mathematics, 354, 2019. 106728.
Google Meet link: https://meet.google.com/jpw-hrwe-evu