Directional metric regularity of multifunctions

van Ngai Huynh (1) , Michel Théra (2)

1 Department of Mathematics, Pedagogical University of Quynhon
2 XLIM-MATHIS - Mathématiques & Sécurité de l'information

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.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

van Ngai Huynh, Michel Théra. Directional metric regularity of multifunctions. Mathematics of Operations Research, 2015, 40 (4), pp.969-991. ⟨10.1287/moor.2014.0705⟩. ⟨hal-01314677⟩