Directional Hölder Metric Subregularity and Application to Tangent Cones

We study directional versions of the Hölderian/Lipschitzian metric subregularity of multifunctions. Firstly, we establish variational characterizations of the Hölderian/Lipschitzian directional metric subregularity by means of the strong slopes and next of mixed tangency-coderivative objects. By product, we give second-order conditions for the directional Lipschitzian metric subregularity and for the directional metric subregularity of demi order. An application of the directional metric subregularity to study the tangent cone is discussed.