Just encountered a very strange problem in my research. It's a nonlinear lasso with constraints. The optimization is
$\min $ $\sum_{t=1}^{T}f\left( y_{t},x_{t};\beta \right) +\lambda \left\Vert \beta \right\Vert $
s.t $C\beta =b,$
where $f\left( \cdot \right) $ is a nonlinear function.
When $f\left( \cdot \right) $ is the norm, then James et al (2015) (http://www-bcf.usc.edu/~gareth/research/CLassoFinal.pdf) gives some hints on the solution path. Is there any reference when $f\left( \cdot \right) $ is nonlinear with constrants. Thanks!