A primal-dual interior point method for nonlinear semidefinite programming

This paper is concerned with a primal-dual interior point method for solving nonlinear semidefinite programming problems. The method consists of the outer iteration (SDPIP) that finds a KKT point and the inner iteration (SDPLS) that calculates an approximate barrier KKT point. Algorithm SDPLS uses a commutative class of Newton-like directions for the generation of line search directions. By combining the primal barrier penalty function and the primal-dual barrier function, a new primal-dual merit function is proposed. We prove the global convergence property of our method. Finally some numerical experiments are given.