Abstract
The general (nonconvex) quadratic multidimensional knapsack problem (QMKP) is one of the most important combinatorial optimization problems with many practical applications. The purpose of this article is to establish equivalent formulations of (QMKP) as so called copositive programs and completely positive programs. The resulting programs can then be handled by copositive programming methods, which are completely different from classical algorithms for directly solving quadratic knapsack problems.
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Acknowledgment
The author would like to thank two anonymous referees for their suggestions that help to improve the first version of this article.
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Nguyen, D.V. (2018). Reformulation of the Quadratic Multidimensional Knapsack Problem as Copositive/Completely Positive Prorams. In: Le, NT., van Do, T., Nguyen, N., Thi, H. (eds) Advanced Computational Methods for Knowledge Engineering. ICCSAMA 2017. Advances in Intelligent Systems and Computing, vol 629. Springer, Cham. https://doi.org/10.1007/978-3-319-61911-8_2
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DOI: https://doi.org/10.1007/978-3-319-61911-8_2
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