An interior point method with a primal-dual quadratic barrier penalty function for nonlinear semidefinite programming

In this paper, we consider an interior point method for nonlinear semidefinite programming. Yamashita, Yabe and Harada presented a primal-dual interior point method in which a nondifferentiable merit function was used. By using shifted barrier KKT conditions, we propose a differentiable primal-dual merit function within the framework of the line search strategy, and prove the global convergence property of our method. Keyword. Nonlinear semidefinite programming, Primal-dual interior point method, Primal-dual quadratic barrier penalty function, Global convergence