METRIC REGULARITY OF PARAMETRIC GENERALIZED INEQUALITY SYSTEMS

Abstract

This paper is mainly devoted to applications of modern tools of variational analysis and generalized differentiation to the metric regularity of parametric generalized inequality systems in infinite-dimensional spaces. The basic tools of our analysis involve the Mordukhovich normal coderivatives of set-valued mappings, the limiting subgradient estimate for the marginal functions, and the Ekeland variational principle. Using these tools, we establish new sufficient conditions for the metric regularity of parametric generalized inequality systems. Our results extend the corresponding results in [23] which established some pointbased sufficient conditions for the metric regularity in the Robinson’s sense of implicit multifunctions in finite-dimensional setting.