A. Wachter et Lt. Biegler, Failure of global convergence for a class of interior point methods for nonlinear programming, MATH PROGR, 88(3), 2000, pp. 565-574
Using a simple analytical example, we demonstrate that a class of interior
point methods for general nonlinear programming, including some current met
hods, is not globally convergent. It is shown that those algorithms produce
limit points that are neither feasible nor stationary points of some measu
re of the constraint violation, when applied to a well-posed problem.