Solver doesn't give absolute minimum

The first step in understanding how Solver works is to understand the algorithms behind it. The default algorithms are built on the Newton-Raphson method. I like this tutorial for understanding how NR algorithms work: http://www.cs.utah.edu/~zachary/isp/...ot/Newton.html It is built on the idea of finding roots, but the same principles apply to minima/maxima, because optimization is essentially about finding the roots of the 1st derivative. In essence, it is as your statement says -- go downhill until you get to the bottom of the valley, but the algorithm cannot tell if this valley is the lowest valley or not.

The newer versions of Solver have an option for using a computationally more intense Evolutionary algorithm: http://en.wikipedia.org/wiki/Evolutionary_algorithm I am less familiar with programming these algorithms, but I do understand the basic idea. Where EA's use multiple seed values, I expect that EA's are not as limited in this respect and may be able to explore multiple "valleys"/minima and determine which of the valleys it finds is the lowest.

Getting outside of the "preprogrammed" algorithms, I could see several other possibilities. One could try some kind of Monte Carlo method -- Choose 1000 or so random seed values, then use an NR algorithm on each of those seed value to find a minimum. Then compare the 1000 or so minima you have and see what that tells you about the global minimum.

I don't know about becoming rich and famous developing these kinds of algorithms, because we have different algorithms already available and tested. What I have given here only scratches the surface of the vast field of numerical analysis and numerical methods. Solver is a good utility with a few different algorithms built into it, but it does not begin to completely cover the field of possible algorithms. I'm not in a position right now to look at your specific case, but there are plenty of algorithms to apply, you just need to try different algorithms until you find one that works (at least most of the time).