A Globally Convergent Interior-Point Algorithm For Inequality-Constrained Nonlinear Semidefinite Programming

We present a globally convergent interior point algorithm for solving nonlinear semidefinite programming with inequality constraint. The method uses an exact penalty function as the merit function. In order to determine the search directions, the algorithm uses the Newton method to solve the KKT system when solving the barrier problems. After linearizating and symmetrizing, the search directions are derived. Under the suitable conditions, it is shown that every limit point of the sequence generated by the algorithm is a Karush-Kuhn-Tucker point of the original problem.