Hi Dimitri,

Your problem has little to do with local versus global optimum.  You can convince yourself that the solution you got is not even a local optimum by checking the gradient at the solution.

The main issue is that your objective function is not differentiable everywhere.  So, you have 2 options: either you use a smooth objective function (e.g. squared residuals) or you use an optimization algorithm than can handle non-smooth objective function.

Here I show that your problem is well solved by the `nmkb' function (a bound-constraints version of Nelder-Mead simplex method) from the "dfoptim" package.

library(dfoptim)

> myopt2 <- nmkb(fn=myfunc, par=c(0.1,max(IV)), lower=0)
> myopt2
$par
[1] 8.897590e-01 9.470163e+07

$value
[1] 334.1901

$feval
[1] 204

$restarts
[1] 0

$convergence
[1] 0

$message
[1] "Successful convergence"

Then, there is also the issue of properly scaling your function, because it is poorly scaled.   Look how different the 2 parameters are - they are 7 orders of magnitude apart.  You are really asking for trouble here.

Hope this is helpful,
Ravi.

-------------------------------------------------------
Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology School of Medicine Johns Hopkins University

Ph. (410) 502-2619
email: rvaradhan@jhmi.edu<mailto:rvaradhan@jhmi.edu>


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