On two variants of calmness and their verification in a class of solution maps

Jiří Outrata, H.Gfrerer (J.Kepler Universitaet Linz)

The talk deals with two strengthened variants of the standard calmness property in connection with solution maps to a class of parameterized constraint- and variational systems. As to the first one, called isolated calmness, several new results from the second-order variational analysis will be presented. They facilitate the application of the Levy-Rockafellar criterion in case of examined solution maps. The second notion, which we term two-sided calmness, requires, in addition, a „reverse“ condition, which enables us to use this property, e.g., in post-optimal analysis. In the framework of an implicit (multi)function model a sufficient condition for this property will be provided and illustrated via a parameterized constraint system.