Document Type

Technical Report


This paper mainly concerns the study of a large class of variational systems governed by parametric generalized equations, which encompass variational and hemivariational inequalities, complementarity problems, first-order necessary optimality conditions, and other optimization-related models important for optimization theory and applications. An efficient approach to these issues has been developed in our preceding work [1] establishing qualitative and quantitative relationships between conventional metric regularity jsubregularity and Lipschitzian/calmness properties in the framework of parametric generalized equations in arbitrary Banach spaces. This paper provides, on one hand, significant extensions of the major results in [1] to new partial metric regularity and hemiregularity properties. On the other hand, we establish enhanced relationships between certain strong counterparts of metric regularity /hemiregularity and single-valued Lipschitzian localizations. The results obtained are new in both finite-dimensional and infinite-dimensional settings.

Number in Series



Applied Mathematics | Mathematics


This research was partially supported by MICINN of Spain, grant MTM2008-06695-C03-01 and program "Juan de la Cierva"; and by the US National Science Foundation under grant DMS-0603846.