Suppose i have the following quadratic program, which needs to be solved for y :
$$\min y'Ay + b'y \text{ s.t: } Gy \ge h$$
Where $A$ is a $n$ by $n$ diagonal matrix, $y$ and $b$ are n-dimensional vectors, and $G$ is a $m_G$ by $n$ matrix and $h$ is a $m_G$-dimensional vector.
Is there a way i could convert my inequality constraints into somthing that will look like box-constraints on the variables $y_i$, on the form :
$$\forall i, a_i \le y_i \le b_i$$
Note that the only thing i know about $G$ is that $m_G > n$. I am open to use a change of variable and modify $A$ and $b$, but i cant find the way to do it.
First guess : I might have to use some kind of basis of the affine half-space defined by $Gy>=h$.