A Primal-Dual Interior-Point Algorithm Based On Decomposition For Nonlinear Semidefinite Programming

We present a primal-dual interior point algorithm based on decomposition for solving nonlinear semidefinite programming problems. The algorithm approxi-mately solves an equality constrained barrier subproblem by computing a range-space step and a null-space step in every iteration. The method uses a combination of the l2-exact penalty function and the primal-dual penalty function as the merit function. It is proved, without assuming the linear independence of the gradients of the equality constraints, if the penalty parameter is bounded, then every limit point of the sequence generated by the algorithm is a KKT point.