On the Aubin property of a class of parameterized variational systems

The paper deals with a new sharp criterion ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class includes parameter-dependent variational inequalities with non-polyhedral constraint sets and also parameterized generalized equations with conic constraints. The new criterion requires computation of directional limiting coderivatives of the normal-cone mapping for the so-called critical directions. The respective formulas have the form of a second-order chain rule and extend the available calculus of directional limiting objects. The suggested procedure is illustrated by means of examples.Comment: 20 pages, 1 figur

On computation of limiting coderivatives of the normal-cone mapping to inequality systems and their applications

The paper concerns the computation of the limiting coderivative of the normal-cone mapping related to $C^{2}$ inequality constraints under weak qualification conditions. The obtained results are applied to verify the Aubin property of solution maps to a class of parameterized generalized equations