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I was wondering whether it is possible to regularize (L1 or L2) non-linear parameters in a general regression model. Say, I have the following non-linear least squares cost function, where $p$ is a $3d$ vector of fitting parameters:

$cost(p_i) = ( y(x) - sin^{p_1}(x) + p{_2}e^{(p_3*x)} )^2$

In the above cost function, $p_1$ and $p_3$ are non-linear parameters. How should I go about regularizing them? If they were linear, I can just sum them up together with the linear parameters (absolute values or squares) and add as a penalty to the cost function, right? However, I'm not sure if I'm allowed to do so for non-linear parameters.

Has anyone considered this problem?

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