Thread Subject: Optimization of 2 variables without empirical equation

I have 2 input variables say 'x' and 'y'. For each input of 'x' and 'y', I get an resultant error 'z'. As an example, 'x' has values 1:1:10 and 'y' has 10:10:100. So the base is an 10x10 matrix. At each of these 100 nodes, I find the resultant error and my aim is to find optimum 'x and y' to minimize error. Now since I don't have a proper empirical relation between x,y and z, I am unable to use any of the multi-variable optimization techniques like Deepest secant, Newton, Nelder-Mead,etc. I have tried to implement 2-D interpolation of x,y and z and then using the minimum of z, but the fit is only reasonable with some inaccuracy.
  
             Any other technique to find the actual minimum?

Thanks.
Vinay

"Vinaykumar " <vin1009@yahoo.com> wrote in message <heb8oq$bd6$1@fred.mathworks.com>...
> I have 2 input variables say 'x' and 'y'. For each input of 'x' and 'y', I get an resultant error 'z'. As an example, 'x' has values 1:1:10 and 'y' has 10:10:100. So the base is an 10x10 matrix. At each of these 100 nodes, I find the resultant error and my aim is to find optimum 'x and y' to minimize error. Now since I don't have a proper empirical relation between x,y and z, I am unable to use any of the multi-variable optimization techniques like Deepest secant, Newton, Nelder-Mead,etc. I have tried to implement 2-D interpolation of x,y and z and then using the minimum of z, but the fit is only reasonable with some inaccuracy.
>
> Any other technique to find the actual minimum?

 
There is no well-defined minimum without some interpolation model to describe how the function behaves between the nodes. Since the possible inter-node behavior is non-unique, so are the possibilities for the minimum.