 
Summary: Mathematical Programming manuscript No.
(will be inserted by the editor)
Kurt M. Anstreicher · Samuel Burer
Computable representations for convex hulls
of lowdimensional quadratic forms
the date of receipt and acceptance should be inserted later
Abstract Let C be the convex hull of points { 1
x
1
x
T
x F n}. Repre
senting or approximating C is a fundamental problem for global optimization
algorithms based on convex relaxations of products of variables. If n 4 and F
is a simplex, then C has a computable representation in terms of matrices X that
are doubly nonnegative (positive semidefinite and componentwise nonnegative). If
n = 2 and F is a box, then C has a representation that combines semidefiniteness
with constraints on product terms obtained from the reformulationlinearization
technique (RLT). The simplex result generalizes known representations for the
convex hull of {(x1,x2,x1x2)x F} when F 2 is a triangle, while the result
