My problem was like this
Find $u$ to minimize the following objective function :
$\left\| {y - Hu} \right\|_2^2 + {\lambda _1}\left\| u \right\|_2^{} + {\lambda _2}\left\| u \right\|_2^2$
Where ${\lambda _1},{\lambda _2} > 0$
Effort so far from taking the derivative
$ - 2{H^T}y + {H^T}Hu + 2{\lambda _2}u + {\lambda _1}\frac{{{u^T}}}{{\left\| u \right\|}}=0$
I dont know how to solve this equation for u ?