Factor-analysis of nonlinear mappings: p-regularity theory
Tret'yakov, A. and J. E. Marsden
Comm. on Pure and Applied An., 2, 425-445
Abstract:
The paper presents recent advances in p-regularity theory,
which has been developing successfully for the last twenty years.
The main result of this theory gives a detailed description of the
structure of the zero set of an irregular nonlinear mapping.
We illustrate the theory with an application to degenerate problems
in different fields of mathematics, which substantiates the general
applicability of the class of p-regular problems. Moreover,
the connection between singular problems and nonlinear mappings is shown.
Amongst the applications, the structure of p-factor-operations
is used to construct numerical methods for solving degenerate nonlinear
equations and optimization problems.