# Advice on Non-Linear Optimization Methods

1. Sep 30, 2011

### NeedPhysHelp8

Hi all,

Hopefully this is the right section for my post, if not I apologize.

I'm hoping I can just get some advice to help me get started in the right direction. I am trying to do a mathematical inversion for the following:

$$\frac{1}{N(zi)} \frac{dN}{dz}|_{z=zi} = -\frac{2}{zi} - \frac{1}{T(zi)} \frac{dT}{dz}|_{z=zi} - \frac{C}{T(zi)}$$

$$N(zi)$$ are measurements made at a series of altitudes.

There is the above relation between measurements and temperature $$T(zi)$$
So temperature is what I am looking to find from the $$N(zi)$$ measurements. C is just a system constant.

What I am trying to do is guess an initial temperature vector, then minimize the $$\chi^{2}$$ between the measurements and the forward model above. So that once chi square is minimized as much as possible, we can determine the temperatures. I am very new to this, but have done some research into optimization and grid search methods. I was looking in the Marquardt Method listed in Numerical Recipes, but I figured I would post here to see if anyone else has any opinions on what would work the best.

If you guys need any more info just let me know. Thanks!

2. Oct 12, 2011