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Math Help - Questions about Griewank function and its starting point and global minimum

  1. #1
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    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

    but my answer is (-1.57,2.22)

    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?
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  2. #2
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    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.

    Or try evolutionary-type algorithms, or simulated annealing. One excellent book I read recently was this one. Perhaps your library has it.

    Hope this helps.
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