Local convergence of an augmented Lagrangian method for matrix inequality constrained programming

We consider nonlinear optimization programs with matrix inequality constraints, also known as nonlinear semidefinite programs. We prove local convergence for an augmented Lagrangian method which uses smooth spectral penalty functions. The sufficient second-order no-gap optimality condition and a suitable implicit function theorem are used to prove local linear convergence without the need to drive the penalty parameter to 0.