Metric regularity and Lipschitzian stability of parametric variational systems

The paper concerns the study of variational systems described by parameterized generalized equations/variational conditions important for many aspects of nonlinear analysis, optimization, and their applications. Focusing on the fundamental properties of metric regularity and Lipschitzian stability, we establish various qualitative and quantitative relationships between these properties for multivalued parts/fields of parametric generalized equations and the corresponding solution maps for them in the framework of arbitrary Banach spaces of decision and parameter variables.The research of the first author was partially supported by MICINN of Spain, grant MTM2008-06695-C03-01 and program “Juan de la Cierva”. The research of the second author was partially supported by the USA National Science Foundation under grant DMS-0603846