Nonlinear Optimization over a Weighted Independence System
Combinatorics
2009-11-21 v1 Computational Complexity
Discrete Mathematics
Optimization and Control
Abstract
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.
Cite
@article{arxiv.0805.0954,
title = {Nonlinear Optimization over a Weighted Independence System},
author = {Jon Lee and Shmuel Onn and Robert Weismantel},
journal= {arXiv preprint arXiv:0805.0954},
year = {2009}
}