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 ErdsKoRado theorem of Frankl, we show that for d=2, finding a ρn-best solution requires exponential time. © 2011 Elsevier B.V. All rights reserved.
Lee, J., Onn, S., & Weismantel, R. (2011). Intractability of approximate multi-dimensional nonlinear optimization on independence systems. Discrete Mathematics, 311(8–9), 780–783. https://doi.org/10.1016/j.disc.2011.01.029