"A Trust Region Method Based on Interior Point Techniques for Nonlinear Programming "
R. Byrd, J.C. Gilbert, J. Nocedal.
Mathematical Programming A, Vol. 89: pp. 149-185 (2000)
An algorithm for minimizing a nonlinear function subject to nonlinear inequality constraints is described. It applies sequential quadratic programming techniques to a sequence of barrier problems, and uses trust regions to ensure the robustness of the iteration and to allow the direct use of second order derivatives. This framework permits primal and primal-dual steps, but the paper focuses on the primal version of the new algorithm. An analysis of the convergence properties of this method is presented.