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Can't find existing local or global minima using Wolfram Alpha?

Posted 26 days ago
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Consider sqrt(x^2+y^2)+2sqrt(x^2+y^2-2x+1)+sqrt(x^2+y^2-6x-8y+25) I need to find Global or Local minima of this function but Wolfram Alpha doesn't seem to find one but the answer is 1 + 2sqrt(5) and it's global minimum

Am I doing something wrong?

https://www.wolframalpha.com/input/?i=minimum+sqrt%28x%5E2%2By%5E2%29%2B2sqrt%28x%5E2%2By%5E2-2x%2B1%29%2Bsqrt%28x%5E2%2By%5E2-6x-8y%2B25%29

with word "local"

https://www.wolframalpha.com/input/?i=local+minimum+sqrt%28x%5E2%2By%5E2%29%2B2sqrt%28x%5E2%2By%5E2-2x%2B1%29%2Bsqrt%28x%5E2%2By%5E2-6x-8y%2B25%29

Posted 25 days ago

This function seems excessively difficult for the Wolfram Engine solve symbolically - which is what Wolfram|Alpha seems to be trying to do.

I do not know if Wolfram|Alpha can numerically minimize, but here is an example of using a notebook (which is free for small computations like this):

Solving it numerically is fast:

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