Hölder Metric Subregularity with Applications to Proximal Point Method

This paper is mainly devoted to the study and applications of Hölder metric subreg-ularity (or metric q-subregularity of order q ∈ (0, 1]) for general set-valued mappings between infinite-dimensional spaces. Employing advanced techniques of variational analysis and generalized differentiation, we derive neighborhood and pointbased sufficient conditions as well as necessary conditions for q-metric subregularity with evaluating the exact subregularity bound, which are new even for the conventional (first-order) metric subregularity in both finite and infinite-dimensions. In this way we also obtain new fractional error bound results for composite polynomial systems with explicit calculating fractional exponents. Finally, metric q-subregularity is applied to conduct a quantitative convergence analysis of the classical proximal point method for finding zeros of maximal monotone operators on Hilbert spaces.