Complexity of a class of nonlinear combinatorial problems related to their linear counterparts

Complexity of a class of nonlinear combinatorial problems related to their linear counterparts

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Article ID: iaor19972004
Country: Netherlands
Volume: 73
Issue: 3
Start Page Number: 569
End Page Number: 576
Publication Date: Mar 1994
Journal: European Journal of Operational Research
Authors: ,
Keywords: computational analysis, programming: integer, programming: nonlinear
Abstract:

The ultimate purpose of the present 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, the authors set the framework, and prove the result for a class of linear programming problems with bounded feasible sets and their nonlinear counterparts. They 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.

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