Nonlinear Metric Subregularity
Optimization and Control
2018-06-19 v2
Abstract
In this article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can be treated in the framework of the theory of (linear) error bounds for extended real-valued functions of two variables developed in A. Y. Kruger, Error bounds and metric subregularity, Optimization 64, 1 (2015) 49-79. Several primal and dual space local quantitative and qualitative criteria of nonlinear metric subregularity are formulated. The relationships between the criteria are established and illustrated.
Cite
@article{arxiv.1502.06159,
title = {Nonlinear Metric Subregularity},
author = {Alexander Y. Kruger},
journal= {arXiv preprint arXiv:1502.06159},
year = {2018}
}
Comments
26 pages. arXiv admin note: substantial text overlap with arXiv:1411.6414, arXiv:1405.1130