Enhanced metric regularity and Lipschitzian propertiesof variational systems

摘要

This paper mainly concerns the study of a large class of variational systemsgoverned by parametric generalized equations, which encompass variational and hemi-variational inequalities, complementarity problems, first-order optimality conditions, andother optimization-related models important for optimization theory and applications. Anefficient approach to these issues has been developed in our preceding work (AragdnArtacho and Mordukhovich in Nonlinear Anal 72:1149-1170, 2010) establishing qualita-tive and quantitative relationships between conventional metric regularity/subregularity andLipschitzian/calmness properties in the framework of parametric generalized equations inarbitrary Banach spaces. This paper provides, on one hand, significant extensions of themajor results in op.cit. to partial metric regularity and to the new hemiregularity property.On the other hand, we establish enhanced relationships between certain strong counterpartsof metric regularity/hemiregularity and single-valued Lipschitzian localizations. The resultsobtained are new in both finite-dimensional and infinite-dimensional settings.