[R] interpolation and extremum location of a surface

[Clement LAUZIN]

Hello,
I have a x,y,z file.
Z is not corresponding to a simple analytical function of x and y. 
I am trying to find the minimum value of z by a spline interpolation or from a polynomial fit.
I tried the akima package but as the location of the point I am looking for (the minimum) is outside of the convex hull it's not working.
If someone has any idea or any suggestion?
Thank you in advance

Pierre