Let $S$ be a set of vectors defined as $S := \{x \in \mathbb{R}^n_+ : e^Tx = 1\}$. A vectorization of matrix $xx^T$, denoted by $vec(xx^T)$, is a transformation by stacking the columns of $xx^T$ on top of each other, resulting a column vector. Given inputs $q \in \mathbb{R}^{n^2}$, $A \in \mathbb{R}^{m \times {n^2}}$, and $b \in \mathbb{R}^m$, the problem is as follows:
$\min q^Ty \\ s.t. Ay = b \\ y \in Conv\{ vec(xx^T) : x \in S\}$
My approach is to solve the problem with Column Generation Algorithm. However I am not sure how to set up the master and the subproblem of the main problem above, especially with the existence of the last constraint. I will really appreciate any help!
