here is my objective function: \begin{equation*} \begin{aligned} & \underset{}{\text{minimize}} & & \frac{1}{n} \sum_{i=1}^{n} \alpha|x_i| + (1-\alpha)|x_i-c| \\ & \underset{}{\text{s.t.}} && 0 \leq \alpha \leq 1 \end{aligned} \end{equation*}
I am wondering if it is possible to express this as a quadratic problem in order to solve it using the corresponding techniques.
Thanks!