Approximation algorithms for indefinite quadratic programming

Abstract

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