Computation of Graphical Derivative for a Class of Normal Cone Mappings under a Very Weak Condition

Let Γ := {x ∈ R | q(x) ∈ Θ}, where q : R → R is a twice continuously differentiable mapping, and Θ is a nonempty polyhedral convex set in R. In this paper, we first establish a formula for exactly computing the graphical derivative of the normal cone mapping NΓ : R ⇒ R, x 7→ NΓ(x), under the condition that Mq(x) := q(x) − Θ is metrically subregular at the reference point. Then, based on this formula, we exhibit formulae for computing the graphical derivative of solution mappings and present characterizations of the isolated calmness for a broad class of generalized equations. Finally, applying to optimization, we get a new result on the isolated calmness of stationary point mappings.