need help with downhill simplex algorithm

hi,

can anyone pls kindly explain to me, in layman terms, what the nonlinear regression algorithm known as downhill simplex is, and how it works? i have read through the explanations found in Numerical Recipes in C (2nd ed) and a few other references, but they are all saying the same thing: create a simplex with N+1 vertices in an N-dimensional space, and then use procedures such as reflections, expansions, etc to home in on a minimum. sadly, i do not understand what the algorithm does.

specifically:

1. say, the merit function that i want to minimize is of the form y(x) = A exp (x^2) + B cos(Cx) + Dx^0.4, where A-D are the model parameters that i want to optimize. is this considered a multi-dimensional problem, or a single-dimensional problem with multiple variables? i cant find a distinct differentiation between multivariable and multidimensional in my references

2. for the same model function above, what kind of a simplex am i supposed to form? what would the simplex represent in this case?

thanks for any help!

ps: apologies if this is not a suitable forum to post this thread