Different penalty functions for lasso, elastic net, and ridge regression in R

Question

Is their a package that allows me to change the penalty function to say, Huber, or absolute value, instead of quadratic L2 norm, when using regularization such as lasso, ridge, or elastic net in R?

Answer 1

I think there is no package, as of right now, that allows to specify your own formula for the penalization. There are special packages like hqreg or ncvreg that give you some other options. The first one hqreg allows for Huber. The second ncvreg allows for minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD).