[R] relative convergence in 'optim'

[Mauricio Zambrano-Bigiarini]

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 )



Thanks in advance for any help,


Mauricio Zambrano-Bigiarini

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