What algorithm can I use to do a least square minimization of a*e^(-lambda*x)+b where a, lambda and b are unk.

Answer 1

The approach I would follow is this: Let's assume your samples are marked as (x_i, y_i)
First set b as the largest value of x_i. For large values of x, the term ae(-λx) would tend to 0. So for the largest value of x_i, y will be accurate.

Then rewrite your equation as
y_i-b= ae(-λx)
ln (y_i-b)= ln a - λx
Transform ln (y_i-b) to a new variable y'_i, and the problem gets simplified to linear least square minimization.

Answer 2

A formula in closed form for perfect least square minimization does not exist.