relative convergence in 'optim'

2012/11/5 Mauricio Zambrano-Bigiarini <hzambran.newsgroups at gmail.com>:

Dear list,

I have a question related to the correct interpretation of the
relative convergence criterion used by 'optim'.


In the help of the function is it written that:

"reltol:Relative convergence tolerance. The algorithm stops if it is
unable to reduce the value by a factor of reltol * (abs(val) + reltol)
at a step."

and I was wondering if the previous criterion is equivalent to:


abs( val [iter] - val[iter-1] ) / val [iter-1] <= reltol * ( abs( val
[iter] ) + reltol )

OR

abs( val [iter] / val [iter-1] ) <= reltol * ( abs( val [iter] ) + reltol )

OR

abs( val [iter] - val [iter-1] ) <= reltol * ( abs( val [iter] ) + reltol )

Just in case it be useful for somebody else.

From the C code on http://svn.r-project.org/R/trunk/src/appl/optim.c :

...
enough = (f > abstol) &&
fabs(f - *Fmin) > reltol * (fabs(*Fmin) + reltol);
   /* stop if value if small or if relative change is low */
   if (!enough) {
count = n;
*Fmin = f;
   }
...

which I would write in R as:

reltol <- abs( f - f.best ) <= reltol * ( abs(f.best) + reltol )



Cheers,

Mauricio Zambrano-Bigiarini

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