In the definition of gradient descent, its not clear how can we know that there is convergence or we reached a minimum. (local or global). Is it by looking at the graph only?
Convergence is deemed sufficient when the requirements for the loss and accuracy are met by the model using the gradient descent!
The usual tool is to look at a plot of the cost history vs. the number of iterations.
This gives you a view as to whether the cost has stopped significantly decreasing.
Or you could look at whether all of the gradients are approaching zero.
The judgement call comes into play as to how good is “good enough”.