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
Journal: Computability, vol. Pre-press, no. Pre-press, pp. 1-11, 2018