I am applying an iterative method (projected newton) to an optimization problem. Theoretically, the method should converge linearly. I would greatly appreciate it if you could share how should I test the convergence and which stopping criteria should I use?I used the gradient norm (gradient of the objective function) as the stopping criteria but the results look weird. The norm only decreases from 1e-01 to 1e-02 and then stays at 1e-02 forever--the gradient norm does not decrease any more. However, the first order necessary condition for the optimization problem says that the gradient should be zero at the solution --> which means we expect to see really small gradient norm, right? --> **Is the gradient norm of order 1e-02 small enough or still big?**Thank you so much!
How to test convergence of an algorithm for constrained optimization
optimization;iterative method;convergence;constrained optimization