Let $y,\alpha\in\mathbb{R}^n$ be $n$-dimensional vectors and $k>0$ be a positive constant. My goal is to minimize
$$k\sum\limits_{i=1}^n|x_i-y_i|-\alpha^Tx$$
with some linear constraints on $x \in \mathbb{R}^n$. Does anyone know how to put this problem in a standard form? Thanks.
Write as an equivalent LP: $\min_{x,z \in \mathbb R^n} \{ k \sum_i z_i - \alpha^T x | x_i - y_i \le z_i, y_i-x_i \le z_i \}$.