Metric Subregularity and Constraint Qualifications for Convex Generalized Equations in Banach Spaces

Metric Subregularity and Constraint Qualifications for Convex Generalized Equations in Banach Spaces

Several notions of constraint qualifications are generalized from the setting of convex inequality systems to that of convex generalized equations. This is done and investigated in terms of the coderivatives and the normal cones, and thereby we provide some characterizations for convex generalized equations to have the metric subregularity. As applications, we establish formulas of the modulus ...

Metric Subregularity for Subsmooth Generalized Constraint Equations in Banach Spaces

Metric Subregularity and Calmness for Nonconvex Generalized Equations in Banach Spaces

This paper concerns a generalized equation defined by a closed multifunction between Banach spaces, and we employ variational analysis techniques to provide sufficient and/or necessary conditions for a generalized equation to have the metric subregularity (i.e., local error bounds for the concerned multifunction) in general Banach spaces. Following the approach of Ioffe [Trans. Amer. Math. Soc....

Metric subregularity for proximal generalized equations in Hilbert spaces

In this paper, we introduce and consider the concept of the prox-regularity of a multifunction. We mainly study the metric subregularity of a generalized equation defined by a proximal closed multifunction between two Hilbert spaces. Using proximal analysis techniques, we provide sufficient and/or necessary conditions for such a generalized equation to have the metric subregularity in Hilbert s...

Metric Subregularity for Nonclosed Convex Multifunctions in Normed Spaces

In terms of the normal cone and the coderivative, we provide some necessary and/or sufficient conditions of metric subregularity for (not necessarily closed) convex multifunctions in normed spaces. As applications, we present some error bound results for (not necessarily lower semicontinuous) convex functions on normed spaces. These results improve and extend some existing error bound results. ...