An Improved Analysis of Semidefinite Approximation Bound for Nonconvex   Nonhomogeneous Quadratic Optimization with Ellipsoid Constraints
  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. 
Yong Xia, Shu Wang, Zi Xu
math.OC