Complexity of a Class of Nonlinear Combinatorial Problems Related to Their Linear Counterparts
European Journal of Operational Research, Vol. 73, No. 3, pp. 569-576, March 1994
8 Pages Posted: 8 Apr 2008 Last revised: 10 May 2017
Date Written: 1994
Abstract
The ultimate purpose of our analysis is to show that for any class of linear combinatorial problems assumed to be NP-hard, the class of their strictly nonlinear counterparts is also NP-hard. In this paper, we set the framework, and prove the result for a class of linear integer programming problems with bounded feasible sets and their nonlinear counterparts. We also discuss briefly the complications that may arise when the feasible set is unbounded, and as a result some strictly nonlinear problems become easy even though their linear versions are hard.
Keywords: Complexity theory, Integer programming, Combinatorial optimization, Nonlinear objective functions, NP-hard
JEL Classification: M11, C61
Suggested Citation: Suggested Citation