As part of my research in statistics, I recently stumbled upon this paper1 which provides an operational perspective into linear models.
In simple linear regression, quadratic programming can be used to solve the problem where for least squares, the objective is $$\begin{array}{ll} \min & Q(\beta) = (Y-X\beta)'(Y-X\beta)\\ \text{s.t.} & A\beta\ge C \\ & \beta \ge 0 \end{array}$$ The notation should be fairly self-explanatory.
However, for nonlinear regression, things are more complicated. For example, the Michaelis-Menten model is multivariate, given by $f(x,\beta)=\beta_1 x/(\beta_2+x)$. It is possible to transform any nonlinear model to a linear one, but there is an element of risk as the errors are altered.
Is there any literature that provides a procedure on how to tackle this type of regression?
Reference
[1] Wang, D. Q., Wu, B. (2006). Teaching Linear Models Based on Operations Research in Statistical Education. ICOTS-7.