Global convergence analysis of line search interior point methods for nonlinear programming without regularity assumptions∗

It has been noticed by Wächter and Biegler that a number of interior point methods for nonlinear programming based on line search strategy may generate a sequence converging to an infeasible point. We show that by adopting a suitable merit function, a modified primal-dual equation, and a proper line search procedure, a class of interior point methods of line search type will generate a sequence such that either all limit points of the sequence are KKT points, or one of the limit points is a FritzJohn point, or one of the limit points is an infeasible point that is a stationary point of minimizing a function that measures the extent of violation to the constraint system. The analysis does not depend on regularity assumptions on the problem. Instead, it uses a set of satisfiable conditions on the algorithm’s implementation to derive the desired convergence property.