How to re-parametrize for quadratic minimization? Given a real-rectangular matrix $S$ and inorder to solve this simple quadratic programming problem: 
Minimize $w'S'Sw = \|S w\|^2$ over $w$ subject to
 $e^Tw = 1$ and $w \geq 0$ 
using a solver I want a re-parametrization of the problem to the form:
$min(-d^T b + 1/2 b^T D b)$ with the constraints 
$A^T b \geq b_0$ 
so that I can use a general purpose optimization software for quadratic programming.
Question: So now, what would $d,b,D,A,b_0$ be? 
Secondly, how is this re-parametrization done (is there a well known procedural, aspect to this or is it just algebra)? I ask because, I would want to use this general purpose solver for various quadratic minimization programs.
I can see that $b$ is $w$ and I am guessing that $A$ is an identity matrix and $b_0$ is a vector of zeros. What is D?

Obviously, $d=0$, $b=w$ and $D=S^{*}S$. As for the equality constraint,
$$
e^{T}w=1\iff e^{T}w\geq1\hspace{1em}\text{and}\hspace{1em}-e^{T}w\geq-1.
$$
Therefore, your $A$ is (in block-matrix form)
$$
A=\left[\begin{array}{c}
e^{T}\\
-e^{T}\\
I
\end{array}\right]
$$
and your $b_{0}$ is
$$
b_{0}=\left[\begin{array}{c}
1\\
-1\\
0\\
\vdots\\
0
\end{array}\right].
$$
