The function is

f(s,t) = ( a1*t + a2*t^2 + ( a3*t + a4*t^2 )*d1*s^2*t^2 + (a5*t +
a6*t^2)*d1^2*b^4*t^4 )*exp(-0.5*d1*s^2*t^2) + a8

where a1,a2,...,a8,d1 are some constants (can be positive or negative),
which are computed from a given set of data.

The objective is to find the minimum value of s >0.5, which satisfies f(s,t)
>0 where t can be any value on the real line. It may be that such s does not
exist for the given dataset

If the conditions f(s,t)>0 and s>0.5 were not needed, then optim could be
used to find the minimum values for both (s,t) with the range setting at
-Inf and Inf.

I suppose one way to do it (I haven't tried out) is to substitute the values
of (s,t) found and see if they satisfy f(s,t)>0, but it may be that s found
is < 0.5, and there is another one just >0.5 There are also other potential
problems and computational disadvantages.


2008/4/24 Paul Smith <phhs80@gmail.com>:

> On Wed, Apr 23, 2008 at 8:51 PM, Kevin Lu <kecactus@googlemail.com> wrote:
> >  I need to find the minimum value of the parameter, s, such that the
> function
> >  f(s,t) > 0 (where -Inf < t < Inf)
> >
> >  I've looked into optim, constrOptim and others but they don't seem to do
> >  this. Des anyone have some suggestions?
>
> In order to allow us to help you, please send us a minimal example.
>
> Paul
>
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