APPROXIMATION ALGORITHMS FOR INDEFINITE QUADRATIC-PROGRAMMING

We consider epsilon-approximation schemes for indefinite quadratic programming. We argue that such an approximation can be found in polynomial time for fixed epsilon and t, where t denotes the number of negative eigenvalues of the quadratic term. Our algorithm is polynomial in 1/epsilon for fixed t, and exponential in t for fixed epsilon. We next look at the special case of knapsack problems, showing that a more efficient (polynomial in t) approximation algorithm exists.