I am doing Monte Carlo study of the simulated method of moments estimator for my economic model. Since the objective function is not differentiable, I am using adaptive_de_rand_1_bin_radiuslimited in BlackBoxOptim.jl as the solver. The value of the objective function at the true parameters is about 1.0.
I noticed that there is no significant progress in fitness reduction after certain steps, although the fitness is still much higher than 1.0. For example, in my 20 Monte Carlo replications, the progress nearly stopped when fitness is between 10.0 to 150.0.
Since there are 15 parameters in my model, it is not easy to know the shape of the objective function. However, I noticed that when I just increase one parameter by 10% from the true value, the fitness jumps from 1.0 to over 300.0.
I know there is a last mile problem in BlackBoxOptim.jl. So, I plan to use Nelder-Mead algorithm in NLopt.jl. Beside the parameter solution from BlackBoxOptim.jl which becomes the initial guess of Nelder-Mead, I wonder what extra information I can bring from BlackBoxOptim.jl to Nelder-Mead?