Re: Optimization Problem - Need Stochastic Method

• To: mathgroup at smc.vnet.net
• Subject: [mg50389] Re: Optimization Problem - Need Stochastic Method
• From: sean_incali at yahoo.com (sean kim)
• Date: Wed, 1 Sep 2004 01:49:32 -0400 (EDT)
• References: <ch1khq\$icv\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```not that i'm an expert in this and it's hard to answer without seeing
the system, but ...

NMinimize comes with various methods, and nelder mead is just one
method it can use. it has random search, simulated annealing etc. It
has an advanced documentation section that details this.

with SimulatedAnnealing you can change the step size and the cooling
schedule as well. (PerturbationScale and BoltzmannExponent)

if built in methods do not work then you can see if it's posible to
implement a steepest gradient descent that uses randon numbers as
starting points.  and repeat over big sample space and see if
different starting points will give you a better convergence.( seems
like a bit of work though)

sean

"David Mebane" <david.mebane at mse.gatech.edu> wrote in message news:<ch1khq\$icv\$1 at smc.vnet.net>...
> Hi All,
>
> I just started using Mathematica - and I'm hoping that there's a nice trick
> I can use to get my optimization done.
>
> The problem is in stereology - I'm an engineering grad student and I have
> developed a bivariate size-orientation unfolding equation for cylinders.
> The equation is extremely complex - a double-integral equation of about 14
> terms.  In addition, there is a stability problem, meaning that for
> practical purposes, the problem is ill-posed.
>
> Because I need to graduate (this is basically a side project gone mad) I am
> getting around the problems of finding a solution and dealing with the
> ill-posedness by simply fitting a distribution that takes a form similar to
> a bivariate normal distribution to the equation.  This means that I have to
> fit 5 distribution parameters to the experimental data, of which there are
> about 25 points.  This makes for a well-overdetermined system, and I have
> constructed a square-error function in Mathematica that is a function of the
> parameters I need to optimize.
>
> Here's the problem: I tried to use constrained NMinimize, but it did not
> converge well - when I plotted the solution graphically against the data
> points, there was severe and systematic error.  I have no idea how the
> fitting function behaves since it's impossible to visualize, but as
> described earlier it's extremely complicated when written out, and it
> involves trig functions and exponentials, so I wouldn't assume that there
> are no local minima.  I think that the best thing to do is to use a
> stochastic method as the search algorithm instead of the default
> Nelder-Mead, but I am not sure if one exists.
>
> Can anyone help?
>
>
> Thanks

```

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