  In this paper, we study augmented Lagrangian functions for nonlinear
semidefinite programming (NSDP) problems with exactness properties. The term
exact is used in the sense that the penalty parameter can be taken
appropriately, so a single minimization of the augmented Lagrangian recovers a
solution of the original problem. This leads to reformulations of NSDP problems
into unconstrained nonlinear programming ones. Here, we first establish a
unified framework for constructing these exact functions, generalizing Di Pillo
and Lucidi's work from 1996, that was aimed at solving nonlinear programming
problems. Then, through our framework, we propose a practical augmented
Lagrangian function for NSDP, proving that it is continuously differentiable
and exact under the so-called nondegeneracy condition. We also present some
preliminary numerical experiments.
