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MathGroup Archive 2005

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Numerical Optimization involving equation solving

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55969] Numerical Optimization involving equation solving
  • From: "Brian Rogers" <brifry at gmail.com>
  • Date: Tue, 12 Apr 2005 05:26:28 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I need to optimize a function of one variable, say
f[x_]:=(stuff;Return[ans];).  Computing the value of f requires solving
a (non-linear) system of equations that depend on x, and using this
solution to compute some other things.

Now, evaluating f at a numerical value of x works just fine, and I can
even plot f (using Plot[f[x],{x,0,1}]) and eyeball the optimum.  By the
way, f is a very well behaved function--it is typically smooth and
globally convex.  However, what I really want to do is use FindMinimum
(or NMinimize) to numerically return the optimum.  When I use either of
these built-in functions, they crash.  I believe that they are first
trying to evaluate f[x] symbolically--which would understandably cause
it to crash because the system of equations doesn't have a closed form
solution in x.

I've tried using the "Compiled" option with no luck.  How can I force
FindMinimum to use a purely numerical procedure to optimize my
function?

Any help is greatly appreciated, and please copy any reply to
brifry at gmail.com.
Thanks!


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