%0 Journal Article
%T Nonlinear Optimization over a Weighted Independence System
%A Jon Lee
%A Shmuel Onn
%A Robert Weismantel
%J Mathematics
%D 2008
%I arXiv
%X We consider the problem of optimizing a nonlinear objective function over a weighted independence system presented by a linear-optimization oracle. We provide a polynomial-time algorithm that determines an r-best solution for nonlinear functions of the total weight of an independent set, where r is a constant that depends on certain Frobenius numbers of the individual weights and is independent of the size of the ground set. In contrast, we show that finding an optimal (0-best) solution requires exponential time even in a very special case of the problem.
%U http://arxiv.org/abs/0805.0954v1