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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! = )

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Well, it is a nonlinear least squares problem, in which case there are a number of excellent algorithms (Gauss-Newton, Levenberg-Marquardt, etc.) for finding solutions numerically. See this as well. –  J. M. Jun 2 '11 at 4:37
    
Thank you, the link is very helpful. –  Phonon Jun 2 '11 at 14:04

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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.

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Thanks. Looks like a great book. Don't know why I've never heard of it. –  Phonon Jun 2 '11 at 14:05

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