# Chebyshev approximation to standard linear programming form

I'm looking for a way to write Chebyshev approximation in standard linear programming form,

Let's say my Chebyshev approximation have the following for:

$$min_{p,t} t$$
s.t.
$$-t1_T \le h - Fp \le t1_T$$

when $$t\in\mathbb{R}; 1_T=\begin{bmatrix}1\\\vdots\\1\end{bmatrix}; h\in\mathbb{R}^T; p\in\mathbb{R}^n; F\in\mathbb{R}^{T\times n}$$

I'm trying to write it the following form:

$$min_{x} c^T x$$
s.t.
$$Ax \le b$$

when $$x,b,c$$ are vectors and $$A$$ is a matrix

my steps are:

$$min_{p,t} t$$
s.t.
$$-t1_T \le h - Fp \land h - Fp \le t1_T$$

$$min_{p,t} t$$
s.t.
$$Fp - h \le t1_T \land h - Fp \le t1_T$$

$$min_{p,t} t$$
s.t.
$$\begin{bmatrix}Fp - h\\h - Fp\end{bmatrix} \le t\begin{bmatrix}1_T\\1_T\end{bmatrix}$$

$$min_{p} \begin{bmatrix}Fp - h\\h - Fp\end{bmatrix} \le \begin{bmatrix}1_T\\1_T\end{bmatrix}$$

so: $$c^T = \begin{bmatrix}1_T\\1_T\end{bmatrix}; x = \begin{bmatrix}p\\p\end{bmatrix}; b = \begin{bmatrix}-h\\h\end{bmatrix}; A = \begin{bmatrix}-F\\F\end{bmatrix}$$

Is it right?