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 mapping 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 for nonlinear programming
for semidefinite programming.