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 its global convergence property under weaker assumptions than the method of Yamashita, Yabe and Harada.