Approximation Algorithms for Quadratic Programming

We consider the problem of approximating the global minimum of a general quadratic program (QP) with n variables subject to m ellipsoidal constraints. For m = 1, we rigorously show that an-minimizer, where error 2 (0; 1), can be obtained in polynomial time, meaning that the number of arithmetic operations is a polynomial in n, m, and log(1==). For m 2, we present a polynomial-time (1 ? 1 m 2)-approximation algorithm as well as a semideenite programming relaxation for this problem. In addition, we present approximation algorithms for solving QP under the box constraints and the assignment polytope constraints.