  In this work, we propose a new local optimization method to solve a class of
nonconvex semidefinite programming (SDP) problems. The basic idea is to
approximate the feasible set of the nonconvex SDP problem by inner positive
semidefinite convex approximations via a parameterization technique. This leads
to an iterative procedure to search a local optimum of the nonconvex problem.
The convergence of the algorithm is analyzed under mild assumptions.
Applications in static output feedback control are benchmarked and numerical
tests are implemented based on the data from the COMPLeib library.
