  We consider the problem of approximating nonconvex quadratic optimization
with ellipsoid constraints (ECQP). We show some SDP-based approximation bounds
for special cases of (ECQP) can be improved by trivially applying the extened
Pataki's procedure. The main result of this paper is to give a new analysis on
approximating (ECQP) by the SDP relaxation, which greatly improves Tseng's
result [SIAM Journal Optimization, 14, 268-283, 2003]. As an application, we
strictly improve the approximation ratio for the assignment-polytope
constrained quadratic program.
