  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.

Optimization and Control