Find params that minimize function

I have the function

where I know the , and σ

How can I find the two params x and y that minimize the function which variable is ξ ?

[Torsten]

x = Inf, y finite, but arbitrary minimizes the function.

Answer 1

[Thiago Henrique Gomes Lobato]

You can define it as an annonymous function and then call fminsearch to solve it:

e = 5;
xi = [1,2,3,4];
yi = [3,4,5,6];
sigma = 2
fun = @(x,e,xi,yi,sigma) abs(4*e- sum(sqrt( (x(1)-xi).^2-(x(2)-yi).^2  ))/(2*sigma^2));
x0 = [1,1];
[x,fval] = fminsearch(@(x)fun(x,e,xi,yi,sigma),x0)

I changed your function with an abs() function, which I believe it was your intention, otherwise your function has no minimum since it can go to -inf.

[Nicola Caldognetto]

yeah, it may need an abs() but, why have you added the e = 5 ?

[Thiago Henrique Gomes Lobato]

I just added random values to all variables to get a result. From your question I understood that you want to find the x and y that minimizes your function for a given e. If you want also to minimize e you can add it to the optimization function as a parameter, although the resulting function will have infinite local minima.

[Nicola Caldognetto]

gotcha, everything is working

Thanks