Hello, Not sure if I should have made this as an issue in GitHub, but I have some question/suggestion regarding the multi-level single linkage method.
I use NLopt's MLSL-LDS optmization via nloptr R package when working with hidden Markov models (I am an author of seqHMM R package), and when I compared results from global optimization via MLSL versus just local optimization with L-BFGS (which I also used in MLSL), I just realized that MLSL does not seem to perform local optimization using the initial parameter values. If I read the source correctly, they are only used in defining the initial sample somehow (in my own code I also set parameter boundaries based on some heuristics with the initial values), but there is often the case that performing the local optimization with good initial values already finds the global optimum, and the additional global phase is just for the "proof". But now at least in one of my example models it happens so that global optimization via MLSL doesn't find the optimum in reasonable time as it does not check the initial guess at all. So could the algorithm be altered in a way that the local optimization is first performed on the initial guess, and then additional point would be drawn? Either still based on the initial guess or the first local optimization. First option wouldn't interfere with the MLSL itself (just one additional local optimization before proceeding as before) so for back-compatibility it might be safer option, whereas the second option, without understanding the details of the MLSL, seems intuitively good alternative as we might at least be somewhere in the right neighborhood compared to completely bogus initial guess. Best regards, Jouni Helske Department of Mathematics and Statistics P.O. Box 35 (MaD) 40014 University of Jyväskylä Finland
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