On March 13, 2024 at 16:00 EET, Nicholas Pischke (TU Darmstadt) will give a talk in the Proof Mining Seminar.
Title: Generalized Fejér Monotone Sequences
Abstract:
I discuss recent results which provide quantitative and abstract strong convergence results for sequences from a compact metric space satisfying a certain form of generalized Fejér monotonicity where (1) the metric can be replaced by a much more general type of function measuring distances (including, in particular, certain Bregman distances), (2) these distance functions are allowed to vary along the iteration and (3) full Fejér monotonicity is relaxed to a certain partial variant. These novel convergence results are established using a preceding finitary and quantitative theorem which constructs a rate of metastability for the Cauchy property of such sequences. In the context of quantitative information, I also discuss the construction of rates of convergence for such sequences in the context of an additional metric regularity assumption as introduced by Kohlenbach, López-Acedo and Nicolae. At the end of the talk, I will shortly mention two methods from the literature that can be quantitatively analyzed using these results but a major application of the general theorems presented here will be given in a second talk in this seminar.
Google Meet link: https://meet.google.com/jpw-hrwe-evu