  The augmented Lagrangian method (ALM) has gained tremendous popularity for
its elegant theory and impressive numerical performance since it was proposed
by Hestenes and Powell in 1969. It has been widely used in numerous efficient
solvers to improve numerical performance to solve many problems. In this paper,
without requiring the uniqueness of multipliers, the local (asymptotic
Q-superlinear) Q-linear convergence rate of the primal-dual sequences generated
by ALM for the nonlinear semidefinite programming (NLSDP) is established by
assuming the second-order sufficient condition (SOSC) and the semi-isolated
calmness of the Karush-Kuhn-Tucker (KKT) solution under some mild conditions.
