So you terminate after a certain number of iterations, rather than setting a target tolerance. I tried that approach with my real application, but the output was very disappointing. I am minimizing a norm that apparently has many local minima. With the local methods in Optim, I have reached an objective value of 1e-7, after trying many initial points, but with CRSLM, running overnight for 8 hours, I have reached something like 200.0. And following the suggestion in your NLopt website of using the output of the global optimizer as starting values of a local optimizer, I do not reach that minimum of 1e-7, but another point with a larger objective value. Do you have any tips? Perhaps the initial box for the global optimizer is too large? Perhaps I should try another global optimizer?
Aside, I suppose those global optimizers have “long memory” in the sense that they remember the best point reached, as oppose to local optimizers that only remember the last point they have reached. Is that so?