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Higher-order metric subregularity and its applications

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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.

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Authors and Affiliations

  1. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    Boris S. Mordukhovich & Wei Ouyang

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  1. Boris S. Mordukhovich
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  2. Wei Ouyang
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Correspondence to Wei Ouyang.

Additional information

This research was partly supported by the National Science Foundation under Grant DMS-12092508.

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Mordukhovich, B.S., Ouyang, W. Higher-order metric subregularity and its applications. J Glob Optim 63, 777–795 (2015). https://doi.org/10.1007/s10898-015-0271-x

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