  It has recently been shown (Burer, Math. Program Ser. A 120:479-495, 2009)
that a large class of NP-hard nonconvex quadratic programming problems can be
modeled as so called completely positive programming problems, which are convex
but still NP-hard in general. A basic tractable relaxation is gotten by doubly
nonnegative relaxation, resulting in a doubly nonnegative programming. In this
paper, we prove that doubly nonnegative relaxation for binary quadratic
programming (BQP) problem is equivalent to a tighter semidifinite relaxation
for it. When problem (BQP) reduces to max-cut (MC) problem, doubly nonnegative
relaxation for it is equivalent to the standard semidifinite relaxation.
Furthermore, some compared numerical results are reported.
