Directional Hölder Metric Regularity

van Ngai Huynh (1) , Huu Tron Nguyen (1) , Michel Théra (2)

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

This paper sheds new light on regularity of multifunctions through various characterizations of directional Hölder /Lipschitz metric regularity, which are based on the concepts of slope and coderivative. By using these characterizations , we show that directional Hölder /Lipschitz metric regularity is stable, when the multifunction under consideration is perturbed suitably. Applications of directional Hölder /Lipschitz metric regularity to investigate the stability and the sensitivity analysis of parameterized optimization problems are also discussed.

Mots clés: 90C30; 54C60; 47H04; 58C06; Slope · Metric regularity · Hölder metric regularity · Generalized equation · Fréchet subdifferential · Asplund spaces · Ekeland variational principle; Hadamard directional differentiability Mathematics Subject Classification (2000) 49J52; 49J53

Domaines: Optimisation et contrôle [math.OC]

van Ngai Huynh, Huu Tron Nguyen, Michel Théra. Directional Hölder Metric Regularity. 2015. ⟨hal-01183274⟩