  In this paper, we present a stabilized sequential quadratic semidefinite
programming (SQSDP) method for nonlinear semidefinite programming (NSDP)
problems and prove its local convergence. The stabilized SQSDP method is
originally developed to solve degenerate NSDP problems and is based on the
stabilized sequential programming (SQP) methods for nonlinear programming (NLP)
problems. Although some SQP-type methods for NSDP problems have been proposed,
most of them are SQSDP methods which are based on the SQP methods for NLP
problems, and there are few researches regarding the stabilized SQSDP methods.
In particular, there is room for the development of locally fast convergent
stabilized SQSDP methods. We prove not only superlinear but also quadratic
convergence of the proposed method under some mild assumptions, such as strict
Robinson's constraint qualification and second-order sufficient condition.
