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  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  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
Aragón Artacho, Francisco J. and Mordukhovich, Boris S., "Enhanced Metric Regularity and Lipschitzian Properties of Variational Systems" (2010). Mathematics Research Reports. 73.