- Holder Metric Subregularity with Applications to Proximal Point Method G Li(g.liunsw.edu.au) B.S. Mordukhovich(borismath.wayne.edu) Abstract: This paper is mainly devoted to the study and applications of H\"older metric subregularity (or metric $q$-subregularity of order $q\in(0,1]$) 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. Keywords: variational analysis, metric subregularity, generalized differentiation, error bounds, proximal point method Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Citation: Preprint, 2012. Download: [PDF]Entry Submitted: 02/03/2012Entry Accepted: 02/03/2012Entry Last Modified: 02/03/2012Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.