A Robust Primal-Dual Interior-Point Algorithm for Nonlinear Programs

We present a primal-dual interior point algorithm of line-search type for nonlinear programs, which uses a new decomposition scheme of sequential quadratic programming. The algorithm can circumvent the convergence difficulties of some existing interior point methods. Global convergence properties are derived without assuming regularity conditions. The penalty parameter ρ in the merit function is updated automatically such that the search directions are descent directions for the merit function. It is shown that if ρ is bounded, then every limiting point of the sequence generated by the algorithm is a KKT point, whereas if ρ is unbounded, then the sequence has a limiting point which is either a Fritz-John point of the feasible set or an infeasible stationary point of minimizing the `2-norm of infeasibility. Numerical results confirm that the algorithm produces the correct results for some hard problems including the examples provided by Wächter and Biegler and Byrd et al. for which many of the existing line-search type interior point methods have failed to find the right answers.