In successive convex approximation method, can the solution be considered to be an acceptable solution if the algorithm reaches the maximum number of iterations without noticeable convergence? or it must converge to a certain tolerance?
I can’t LaTeX or MathJax this effectively, but you have to pick your own measure of beauty (norm) and how much beauty you require (to quote my PhD advisor). So if a reduction of 5 orders of magnitude in the L2 norm is what you want, use that.
If your answer is still reducing, I wouldn’t stop after a fixed number of steps unless that number was huge and you’re already getting close to machine precision.