Reformulate Ridge and LASSO

$1.$ In lecture, we defined ridge regularization by the minimizer:

L$($c$)=||$y$$Ac$||2+\backslash$lambda $||$c$||2$

Show that this is equivalent to the constrained minimization problem:

L$($c$)=||$y$$Ac$||2(1)$

such that $||$c$||2<=$ t $(2)$

Describe how $\backslash$lambda and t are related.

$2.$ Similarly, we defined LASSO using the minimizer

L$($c$)=||$y$$Ac$||2+\backslash$lambda $||$c$||1$

Show that this is equivalent to the constrained minimization

L$($c$)=||$y$$Ac$||2$

such that $||$c$||1<=$ t

Again describe how $\backslash$lambda and t are related.