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MathGroup Archive 2003

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Re: Numerical Optimization of

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44449] Re: Numerical Optimization of
  • From: Bill Rowe <readnewscix at mail.earthlink.net>
  • Date: Mon, 10 Nov 2003 04:52:19 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 11/9/03 at 6:01 AM, rogers at tanis.hss.caltech.edu (Brian Rogers) wrote:

> I have a function f[x] of one variable that computes it's output by
> solving a system of equations and returning a list of three numbers. 
> So f[x] looks like {f[x][[1]],f[x][[2]],f[x][[3]]}.  When I plot
> f[x][[1]], I get a nice smooth strictly convex function that clearly
> has a global minimum around 6.7.  But when I try to find the minimum
> I can't.  Specifically, using NMinimize[f[x][[1]],{x}] and
> FindMinimum[f[x][[1]],{x,6}] both run forever without returning any
> errors or results. 

In principle, there should be no problems finding the minimum for a function returning using the syntax you've outlined above. The problem is undoubtedly related to the details of your function which you didn't supply. For me to offer any specific guidance, I need the details of the function.

I will note that simply because Mathematica plots a function as strictly convex and smooth does not mean that it actually is strictly convex and smooth. For example consider plotting the function

(x-1)^2 + Abs[x-1]^-.0001

With Mathematica 5.0 on a Mac running OS 10.3, the plot looks strictly convex and smooth when plotted from x = 0 to x = 2. Yet it clearly has a singularity at x = 1. Remeber, Mathematica samples your function and makes assumptions about the behaviour of your function between the sampled points. Regardless of what plotting algorithm is chosen, it will always be possible to find examples where the resulting plot does not accurately reflect the true behaviour of the function.
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