  This paper is concerned with second-order optimality conditions for the
mathematical program with semidefinite cone complementarity constraints
(SDCMPCC).To achieve this goal, we first provide an exact characterization on
the second-order tangent set to the semidefinite cone complementarity (SDCC)
set in terms of the second-order directional derivative of the projection
operator onto the SDCC set, and then use the second-order tangent set to the
SDCC set to derive second-order necessary and sufficient conditions for SDCMPCC
under suitable subregularity constraint qualifications. An application is also
illustrated in characterizing the second-order necessary optimality condition
for the semidefinite rank regularized problem.
