  In this note, we establish superiority of the so-called copositive bound over
a bound suggested by Nesterov for the quadratic problem to minimize a quadratic
form over the l1-ball. We illustrate the improvement by simulation results. The
copositive bound has the additional advantage that it can be easily extended to
the inhomogeneous case of quadratic objectives including a linear term. We also
indicate some improvements of the eigenvalue bound for the quadratic
optimization over the lp-ball with 1<p<2, at least for p close to one.
