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Holder Metric Subregularity with Applications to Proximal Point Method

G Li(g.li***at***unsw.edu.au)
B.S. Mordukhovich(boris***at***math.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: 02/03/2012
Entry Accepted: 02/03/2012
Entry Last Modified: 02/03/2012

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