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-   -   minimum of a function (http://mymathforum.com/complex-analysis/33479-minimum-function.html)

david hilbert January 26th, 2013 10:12 PM

minimum of a function
 
Hello from Greece.

Is there anybody out there who can help on this topic

" determine the minimum of the function f(z) defined where
with z a complex number such us "

Thanks in advance!

CaptainBlack January 27th, 2013 10:53 PM

Re: minimum of a function
 
Have you considered treating this as a constrained minimisation problem in two variables?

CB

CaptainBlack January 27th, 2013 11:15 PM

Re: minimum of a function
 
You have to be carefull how you define the function when since is undefined there, but behaves like .

Also just plotting this over the constrained region shows that the minimum occurs when , and is zero (at least withthe removable singularity at z=0 removed!).

CB

tahir.iman January 28th, 2013 02:33 AM

Re: minimum of a function
 
find the value of z for


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