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HIGHER-ORDER METRIC SUBREGULARITY AND ITS APPLICATIONS

Boris S. Mordukhovich(boris***at***math.wayne.edu)
Wei Ouyang(wei***at***wayne.edu)

Abstract: This paper is devoted to the study of metric subregularity and strong subregularity of any positive order $q$ for set-valued mappings in finite and infinite dimensions. While these notions have been studied and applied earlier for $q=1$ and---to a much lesser extent---for $q\in(0,1)$, no results are available for the case $q>1$. We derive characterizations of these notions for subgradient mappings, develop their sensitivity analysis under small perturbations, and provide applications to the convergence rate of Newton-type methods for solving generalized equations.

Keywords: variational analysis, metric subregularity and strong subregularity of higher order, Newton and quasi-Newton methods, generalized normals and subdifferentials

Category 1: Nonlinear Optimization

Citation: Wayne State University, July,2014

Download: [PDF]

Entry Submitted: 07/14/2014
Entry Accepted: 07/14/2014
Entry Last Modified: 07/14/2014

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