I'm using the Nelder-Mead algorithm for a project. Is there any way I can guarantee that the method will find find the absolute minimum of my function if my function has multiple local minima? Is the method highly dependent on my initial guess?

Maybe this question is assuming a perfect world, but is there any way to find the absolute minimum of a function without having to worry about finding local extrema?

  • $\begingroup$ The only way to find a global min for a general function is to test the function everywhere. If you have Lipschitz continuity, you can get an $\epsilon$-optimal solution by chopping the domain into small hyper-cubes and sampling the function at a corner point of each hyper-cube. Of course, the complexity of this method is exponential in the number of variables. $\endgroup$
    – Michael
    May 3, 2018 at 6:51
  • $\begingroup$ Ok. I'm not sure this will help me, but thanks for the reply. $\endgroup$
    – D.B.
    May 3, 2018 at 15:23


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