Metric Subregularity for Nonclosed Convex Multifunctions in Normed Spaces
نویسندگان
چکیده
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. Mathematics Subject Classification. 90C31, 90C25, 49J52. Received September 13, 2008. Revised February 4, 2009. Published online June 18, 2009.
منابع مشابه
Metric subregularity of multifunctions and applications ∗
The metric subregularity of multifunctions is a key notion in Variational Analysis and Optimization. In this paper, we establish firstly a cretirion for metric subregularity of multifunctions between metric spaces, by using the strong slope. Next, we use a combination of abstract coderivatives and contingent derivatives to derive verifiable first order conditions ensuring the metric subregulari...
متن کاملMetric 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...
متن کاملOn Differentiability of Metric Projections onto Moving Convex Sets
We consider properties of the metric projections onto moving convex sets in normed linear spaces. Under certain conditions about the norm, directional diierentiability (of higher order) of the metric projections at boundary points is characterized. The characterization is formulated in terms diierentiability of multifunctions and properties of the set-derivatives are shown.
متن کاملConvexity and Geodesic Metric Spaces
In this paper, we first present a preliminary study on metric segments and geodesics in metric spaces. Then we recall the concept of d-convexity of sets and functions in the sense of Menger and study some properties of d-convex sets and d-convex functions as well as extreme points and faces of d-convex sets in normed spaces. Finally we study the continuity of d-convex functions in geodesic metr...
متن کاملJOHANNES KEPLER UNIVERSITY LINZ Institute of Computational Mathematics Second Order Conditions for Metric Subregularity of Smooth Constraint Systems
Metric subregularity (respectively calmness) of multifunctions is a property which is not stable under smooth perturbations, implying that metric subregularity cannot be fully characterized by first order theory. In this paper we derive second order conditions for metric subregularity, both sufficient and necessary, for multifunctions associated with constraint systems as they occur in optimiza...
متن کامل