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 $D$?