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no message from Minimize[] on a weird function(x^x) !?!

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  • Subject: [mg96724] no message from Minimize[] on a weird function(x^x) !?!
  • From: congruentialuminaire at yahoo.com
  • Date: Sun, 22 Feb 2009 03:12:39 -0500 (EST)

Hello MathGroup:

I have:

f[x_]=x^x
Plot[f[x],{x,-3,3.}]

What makes this a weird function is that when x<0, the function is
discontinuous and non-differentiable and has a global minimum at -1.

To answer the question: "what is the minimum of this function", I
tried

FindMinimum[f[x],{x,2}] (* this appears correct *)
> {0.692201, {x -> 0.367879}}
FindMinimum[f[x],{x,2}] (* this complains about the gradient, but
appears correct *)
> FindMinimum::nrgnum: The gradient is not a vector of real numbers at {x} = {-1.}. >>
> {-1., {x -> -1.}}
NMinimize[f[x], x] (* this gives the minimum in the positive domain *)
> {0.692201, {x -> 0.367879}}
Minimize[f[x], x] (* this gives no answer and no error message *)
> Minimize[x^x, x]

Is this expected behavior?

TIA.

Roger Williams
Franklin Laboratory


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