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Root search on results of minimization with free parameter

  • To: mathgroup at smc.vnet.net
  • Subject: [mg114770] Root search on results of minimization with free parameter
  • From: Philipp WeiÃgraeber <weissgraeber at fsm.tu-darmstadt.de>
  • Date: Thu, 16 Dec 2010 05:50:36 -0500 (EST)

Hello all!

I have a function f which is for example the result of a minimization with 
respect to x. It still depends on a parameter c. Now I want to find the root 
(or minima or whatever) of the the function f with respect to c. 
This seems does not work. 
I always get the errors "NMinimize::nnum: Function value is not a number" 
resp. "FindRoot::nlnum: The function value is not a list of numbers"

Example:
example[c_, x_] = x^2 + c/2;
f[c_] := NMinimize[example[c, x], x][[1]];
FindRoot[f[c] == 0, {c, 14}]

How can I implement this? 
My original problem is of course of more complex nature, but it boils down to 
this.

Thank you

Philipp


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