I am trying to solve a nonlinear optimization problem using fmincon interior point method. Originally my problem formulation does not have bounds on the decision variable, and when i try to run it without the bounds then it takes infintie time and when I run it with bounds then it is much faster. Following are my questions:
1) Why bounds are making the algorithm faster?
2) The final optimal result for the problem is nowhere near the bound, but my lagrange multiplier for the bounds is coming to be non zero, arent they supposed to be zero if the solution is not hitting the bounds?
3) How is the first order optimality criteria defined for interior point method? I saw the documentation but it is not clear to me, is the infinite norm of the grad or some other equation?
I am giving very good initial guess (exact true values) to my problem to make sure it is near the optimal. When I do that, the optimizer is just giving me the intial guess as my final solution which is not possible as I am feeding noisy data to my problem.
Thanks in advance