A computational study of a class of recursive inequalities

Autor:	Neri, Morenikeji, Powell, Thomas
Rok vydání:	2022
Předmět:	Mathematics - Logic Mathematics - Functional Analysis Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results concerning rates of convergence, setting out conditions under which computable rates are possible, and when not, providing corresponding rates of metastability. We then demonstrate how the aforementioned quantitative results can be applied to extract computational information from a range of proofs in nonlinear analysis. Here we provide both a new case study on subgradient algorithms, and give overviews of a selection of recent results which each involve an instance of our main recursive inequality. This paper contains the definitions of all relevant concepts from both proof theory and mathematical analysis, and as such, we hope that it is accessible to a general audience. Comment: 44 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2207.14559 Zobrazit plný text záznamu View this record from Arxiv