This is a past examination question. I was asked (Q.1) to find an equivalent linear programming problem of:
$$\min_{x \geq 0} \left \|Ax-a \right\|_{1} + \left\|Bx-b \right\|_{\infty}$$
where $A$ is an $m \times n$ matrix, $a$ is in $\mathbb{R}^{m}$; $B$ is an $l \times n$ matrix, $b$ is in $\mathbb{R}^{l}$.
(Q.2) I need to give the KKT conditions of the problem.
(Q.3) I need to formulate the problem to a linear variational inequality.
My puzzle for (Q.1) is about the two different norms used in the minimization problem. Is it a linear programming problem already? Would you please teach me how to do (Q.1)?
I think I can finish (Q.2) if my problem of (Q.1) is solved.
For (Q.3), would you please give me hint to finish it?
Thank you in advance.
