The problem statement is as follows.
Minimize $||g(X\beta)-y||^2$ with respect to $\beta$ where $g(\cdot)$ is some non-linear function, $y$ and $\beta$ are column vectors.
General linear least squares problems are of form $\text{argmin}_\beta\{||X\beta-y||^2\}$ and have plenty of solutions. Simply calling the above problem non-linear least squares produces a myriad of search results and none suits my need. Is there a name for this? Can someone point me in the right direction?
Cheers! = )
You might try any numerical analysis book on multidimensional minimization. I don't think the fact that $\beta$ is a vector as opposed to a set of parameters will help. Section 10.4 and on of Numerical Recipes is one source and the obsolete ones are free.