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Re: no message from Minimize[] on a weird function(x^x) !?!
*To*: mathgroup at smc.vnet.net
*Subject*: [mg96771] Re: no message from Minimize[] on a weird function(x^x) !?!
*From*: dh <dh at metrohm.com>
*Date*: Tue, 24 Feb 2009 05:47:23 -0500 (EST)
*References*: <gnr1d2$ep0$1@smc.vnet.net>
Hi Roger,
your function is more "weird" than you think, but it is not
discontinuous and non-differentiable, except at zero where it is not
defined. What you have is a multi valued complex function. For numerical
calculations mathematica has to pick a branch, what creates problems
with branch cuts. Therefore, it does not make sense to minimize x^x, but
you may e.g. minimize Abs[f[x]].
Therefore, you may minimize e.g. Abs[f[x]].
hope this helps, Daniel
congruentialuminaire at yahoo.com wrote:
> 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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