Good afternoon, my experience in mathematical programming is low. I would like to know if there is any general method to address the following problem:

$$\text{Minimize }\sum_{i=1}^n d_i(x_j)$$ $$s.a.\quad Ax=b,$$ $$~~~~~~~~\qquad x\geq 0,$$ where $A$ is a matrix $m\times n$ with rank $m$, $x\in \mathbb{R}^n$, $b\in\mathbb{R}^m$, and \begin{equation*} d_j(x_j) = \begin{cases} 0, & \text{if $x_j= 0$},\\ d_jx_j+t_j, & \text{if $x_j> 0$}, \end{cases} \end{equation*} $d_j,x_j$ are constants.

Very grateful for your answers and references of the problem mentioned.