Thread: Questions about Griewank function and its starting point and global minimum

1. Questions about Griewank function and its starting point and global minimum

I have a questions regarding Griewank functions..I was asked to use Newton's method to find the minimum of griewank function with the starting point of (-2,2)

Griewank function:

f(x,y) = (x^2+y^2)/4000 -cos(x)*cos(y/sqrt(2)) + 1

since the global minimum of Griewank function is known to be (0,0)
why the starting point (-2,2) does not lead to (0,0)? why is it (-1.57,2.22)?
what had stops to find the global minimum?

2. Local Extrema

Assuming you're correctly using the Hessian method as referenced here in the "Higher Dimensions" section, I would say that it's entirely possible that, given your starting point, you converged on a local minimum. This is the problem with many optimization techniques - certainly Newton's method is susceptible to converging on a local extrema instead of the global one. Newton's method, like many other methods, is highly dependent on your starting point. Try a few other starting points and see if they give you different numbers.