  This paper is devoted to studying the robust isolated calmness of the
Karush-Kuhn-Tucker (KKT) solution mapping for a large class of interesting
conic programming problems (including most commonly known ones arising from
applications) at a locally optimal solution. Under the Robinson constraint
qualification, we show that the KKT solution mapping is robustly isolated calm
if and only if both the strict Robinson constraint qualification and the second
order sufficient condition hold. This implies, among others, that at a locally
optimal solution the second order sufficient condition is needed for the KKT
solution mapping to have the Aubin property.
