Directional H\"older Metric Regularity

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