  This paper is concerned with the strong calmness of the KKT solution mapping
for a class of canonically perturbed conic programming, which plays a central
role in achieving fast convergence under situations when the Lagrange
multiplier associated to a solution of these conic optimization problems is not
unique. We show that the strong calmness of the KKT solution mapping is
equivalent to a local error bound for solutions of perturbed KKT system, and is
also equivalent to the pseudo-isolated calmness of the stationary point mapping
along with the calmness of the multiplier set map at the corresponding
reference point. Sufficient conditions are also provided for the strong
calmness by establishing the pseudo-isolated calmness of the stationary point
mapping in terms of the noncriticality of the associated multiplier, and the
calmness of the multiplier set mapping in terms of a relative interior
condition for the multiplier set. These results cover and extend the existing
ones in \cite{Hager99,Izmailov12} for nonlinear programming and in
\cite{Cui16,Zhang17} for semidefinite programming.
