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.
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