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

In this paper, we are concerned with a primal-dual interior point method for solving nonlinearly constrained optimization problems, in which Newton-like methods are applied to the shifted barrier KKT conditions. We propose a new primal-dual merit function, called the primal-dual quadratic barrier penalty function, framework of line search methods, and show the global convergence properties of our method. Asymptotic superlinear convergence of the method is achieved by carefully controlling the parameters. Some numerical experiments are presented to show the performance of our method.