Consider a vector $a \in R^n$.
I want to know how I can find analytically the solution of the following optimization problem: $x^* = argmin_{x \in R^n} f(x)$, where
- $f(x) = ||x-a||_{2}^2 + \lambda ||x||_1$
- $\lambda > 0$ and
- $||.||_p$ is the p-norm in $R^n$.
Thanks in advance.