A trust-region interior-point method for nonlinear programming

Under mild conditions, the Jacobian associated with the Karush-Kuhn-Tucker (KKT) system of a non-convex, nonlinear program is nonsingular near an isolated solution. However, this property may not hold away from such a solution. To enhance the robustness and efficiency of the primal-dual interior-point approach, we propose a method that at each iteration solves a trust-region, least-squares problem associated with the linearized perturbed KKT conditions. As a merit function, we use the Euclidean norm-square of the KKT conditions and provide a theoretical justification. We present some preliminary numerical results.