## Intractability of approximate multi-dimensional nonlinear optimization on independence systems

We consider optimization of nonlinear objective functions that balance $d$ linear criteria over $n$-element independence systems presented by linear-optimization oracles. For $d=1$, we have previously shown that an $r$-best approximate solution can be found in polynomial time. Here, using an extended Erdos-Ko-Rado theorem of Frankl, we show that for $d=2$, finding a $\rho n$-best solution … Read more

## Nonlinear Optimization over a Weighted Independence System

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 … Read more