Approximation Algorithms for Concave Quadratic Programming

Abstract

We consider $\epsilon$-approximation schemes for concave quadratic programming. Because the existing definition of $\epsilon$-approximation for combinatorial optimization problems is inappropriate for nonlinear optimization, we propose a new definition for $\epsilon$-approximation. We argue that such an approximation can be found in polynomial time for fixed $\epsilon$ and $k$, where $k$ denotes the number of negative eigenvalues. Our algorithm is polynomial in 1/$\epsilon$ for fixed $k$, and superexponential in $k$ for fixed $\epsilon$.