Most formulations of the LCP derived from the KKT conditions of a QP tackle problems with non-negativity constraints $x\ge 0$. Wikipedia presents an alternative without the non-negative constraints but that requires the $Q$ matrix (from the quadratic objective) to be non-singular.
My question is: if one can only assume $Q$ to be positive semidefinite, can we still formulate the problem as an LCP? If so, how?
I tried to find the LCP, but had no luck without assuming at least the existence of a left inverse of $Q$.