I want to efficiently solve the following optimization problem: \begin{align} \min &\quad \left\|\mathbf{x}-\mathbf{x}_0\right\|_2^2 + \lambda\left\|\mathbf{x}\right\|_1\\ \text{Subject to}& \quad A\mathbf{x} \leq c, \end{align}
where $\mathbf{x}\in \mathbb{R}^{n\times 1}$, for big values of $n$. I tried coordinate descend, but it doesn't work. I also don't want to formulate it as QP and use interior-point methods because they are slow. Any idea?