Nonlinear Metric Subregularity
arXiv:1502.06159 · doi:10.1007/s10957-015-0807-8
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.
26 pages. arXiv admin note: substantial text overlap with arXiv:1411.6414, arXiv:1405.1130