# Higher-Order Metric Subregularity and Its Applications

arXiv: https://arxiv.org/abs/1507.04825 · HTML: https://mlsanity.com/paper/1507.04825/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2015.

## Built on by (most cited first, 1 of 1)

- [An inexact LPA for DC composite optimization and application to matrix completions with outliers](https://mlsanity.com/paper/2303.16822/) (2023)

## Abstract (arXiv)

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∈(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.