I want to turn this objective function
$$\max \sum_{i=1}^{N-1} \sum_{j=i+1}^N |TX_i^T - TX_j^T|$$
where $T$ is just a vector with increasing integers (e.g $[1 \ 2]$) and $X_i$ is a vector with $n$ variables like $[x_{11} \ x_{12}]$.
Is there a way to turn this objective function into a linear form?
And how can I do that?
My problem is that I don't quite fully understand it when I have to maximize the objective function.