We present a successive linearization method with a trust region-type
globalization for the solution of
nonlinear semidefinite programs. At each iteration, the method
solves a quadratic semidefinite program, which can be converted to
a linear semidefinite program with a second order cone
constraint. A subproblem of this kind can be solved quite
efficiently by using some recent software for semidefinite and
second-order cone programs. The method is shown to be
globally convergent under certain assumptions. Some numerical
results are included in order to illustrate its behavior.