  This paper is concerned with the positive semidefinite (PSD) composite rank
constraint system. By leveraging its equivalent reformulations, we present
several criteria to identify the calmness of the multifunction associated to
its partial perturbation and discuss the relation among them. Then, a
collection of examples are provided to illustrate that these criteria can be
satisfied for some common PSD composite rank constraint sets. Finally, the
calmness of the associated multifunction is employed to establish the global
exact penalty for the equivalent reformulation of the PSD composite rank
constrained and regularized optimization problems.
