On the reverse mathematics and Weihrauch complexity of moduli of regularity and uniqueness

Issue title: Oberwolfach Workshop on Computability Theory 2018

Guest editors: Vasco Brattka, Rod Downey, Julia F. Knight and Steffen Lempp

Article type: Research Article

Authors: Kohlenbach, Ulrich^{; *}

Affiliations: Department of Mathematics, Technische Universität Darmstadt, Germany. [email protected]

Correspondence: [*] Corresponding author. [email protected].

Abstract: The notion of ‘modulus of regularity’, as recently studied in [Moduli of regularity and rates of convergence for Fejér monotone sequences, 2017, Preprint], unifies a number of different concepts used in convex optimization to establish rates of convergence for Fejér monotone iterative procedures. It generalizes the notion of ‘modulus of uniqueness’ to the nonunique case. In this paper, we investigate both notions in terms of reverse mathematics and calibrate their Weihrauch complexity.

Keywords: Moduli of regularity, moduli of uniqueness, reverse mathematics, Weihrauch complexity, convex optimization

DOI: 10.3233/COM-180097

Journal: Computability, vol. 8, no. 3-4, pp. 377-387, 2019