Question about simplex size in multidimentional minimization.

[Jiasen Guo]

Dear all,
I came across a question regarding the size of the simplex in the
multi-dimensional minimization. Specifically, I am trying to use the
simplex method to minimize a nonlinear non-differentiable function with
multiple variables whose ranges differ by several magnitudes. for example,
V1 ~ 0.1, V2 ~ 10000. I have observed that in order for the algorithm to
work for V1, I have to set the stop criteria, epsabs, much smaller than the
initial value of V1, like 0.001, but such an epsabs will be too strict for
V2. My question here, how is the size of the simplex determined? Is the
scale of the parameter considered when the simplex size is calculated? If I
can not use epsabs as the stopping criteria in such a problem with
parameters spanning multiple orders of magnitude, what other options would
you suggest? Thanks in advance for your kind help.

Best,
Jiasen Guo