  We consider the nonconvex set $\mathcal S_n = \{(x,X,z): X = x x^T, \; x
(1-z) =0,\; x \geq 0,\; z \in \{0,1\}^n\}$, which is closely related to the
feasible region of several difficult nonconvex optimization problems such as
the best subset selection and constrained portfolio optimization. Utilizing
ideas from convex analysis and disjunctive programming, we obtain an explicit
description for the closure of the convex hull of $\mathcal S_2$ in the space
of original variables. In order to generate valid inequalities corresponding to
supporting hyperplanes of the convex hull of $\mathcal S_2$, we present a
simple separation algorithm that can be incorporated in branch-and-cut based
solvers to enhance the quality of existing relaxations.
