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!

**Follow-Ups**:**Re: Numerical Optimization involving equation solving***From:*Chris Chiasson <chris.chiasson@gmail.com>

**Re: Numerical Optimization involving equation solving***From:*Christopher Purcell <christopherpurcell@mac.com>