As we know, in the interior point methods, all the iterates have to be strictly feasible. I implemented an affine scaling interior point for nonlinear objective functions. For small examples (2D), it works as expected. However, for large examples (e.g. optimal control problems), after a finite number of steps, some elements of the iterates start to be on the boundaries. I don't know the exact solutions of those optimal control problems, so I compared the results with the other methods (i.e. same problems, different methods). The numerical solutions obtained from this interior point method have the same number of active elements as the solutions obtained from the other methods. The solutions have the same plots as well as objective function values. The issue here is why the iterates are not strictly feasible. (they are for small examples but not for examples with large numbers of variables).
In short, the method of interest (i.e. interior point method) produces the same numerical solutions as the other methods but the iterates are not strictly feasible. Could you please help me?