- Intractability of approximate multi-dimensional nonlinear optimization on independence systems Jon Lee (jonleeus.ibm.com) Shmuel Onn (onnie.technion.ac.il) Robert Weismantel (weismantmath.uni-magdeburg.de) Abstract: 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 requires exponential time. Keywords: Erdos-Ko-Rado theorem, intractability, nonlinear discrete optimization Category 1: Other Topics (Multi-Criteria Optimization ) Category 2: Combinatorial Optimization (Approximation Algorithms ) Category 3: Combinatorial Optimization (Graphs and Matroids ) Citation: IBM Research Report RC24938 (January, 2010) Download: [PDF]Entry Submitted: 01/29/2010Entry Accepted: 01/29/2010Entry Last Modified: 02/01/2010Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society.