Directional metric regularity of multifunctions

Huynh van Ngai (1) , Michel Théra (2)

1 Department of Mathematics, Pedagogical University of Quynhon
2 XLIM-DMI - DMI

In this paper, we study relative metric regularity of set-valued mappings with emphasis on directional metric regularity. We establish characterizations of relative metric regularity without assuming the completeness of the image spaces, by using the relative lower semicontinuous envelopes of the distance functions to set-valued mappings. We then apply these characterizations to establish a coderivative type criterion for directional metric regularity as well as for the robustness of metric regularity.

Mots clés: Generalized equations; Error bound; Perturbation stability; relative/directional metric regularity; Semicontinuous envelope; Generalized equations.

Domaines: Optimisation et contrôle [math.OC]; Analyse classique [math.CA]

Huynh van Ngai, Michel Théra. Directional metric regularity of multifunctions. 2013. ⟨hal-00818475⟩