# Algorithm for finding the minimum in R

If the minimum is not unique and the MLE is equal to zero over a range of functions, how can we find the minimum? I have read about golden section search algorithm or bisection algorithm, but I don't know if they would apply in this case or not? Is there any other better algorithm which is faster than these algorithms in R?

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Uuuhh.. ? If the minimum is not unique then THE minimum does not exist. Do you mean there are several local minima ? What do you mean by "zero over a range of functions" ? Do you have an example of such a likelihood ? – Stéphane Laurent Jul 16 '12 at 7:05
When you say "the minimum is not unique" I hope you mean that there are multiple local minima but still a unique global minimum. In that situation, you could try starting your minimization algorithm from several different parts of the space to see where the "lowest" converged point is. In general, there is no silver bullet to handling optimization problems involving multi-modal functions but these kinds of informal procedures are useful. – Macro Jul 16 '12 at 14:29

I think you should look at the quasi-newton optimization through the function optim() function. You should also look at the packages and function listed under the optimization cran task view: http://cran.r-project.org/web/views/Optimization.html