互补背包问题的一类新的方面
New Classes of Facets for Complementarity Knapsack Problems
摘要：
互补背包问题（CKP）是一个具有实值变量和其变量对之间的互补条件的背包问题。我们扩展了德法里亚斯等人的多面体研究。CKP，提出了三个新的家庭的切割平面，都是从一个组合的概念被称为包。基于最大交换包的概念，给出了这些不等式是分面定义的充分条件。此外，我们还肯定地回答了de Farias等人的一个猜想。关于分离的复杂性的不等式介绍了他们的工作，并提出了有效的分离算法，我们新定义的切割平面。
英文摘要：
The complementarity knapsack problem (CKP) is a knapsack problem with real-valued variables and complementarity conditions between pairs of its variables. We extend the polyhedral studies of De Farias et al. for CKP, by proposing three new families of cutting-planes that are all obtained from a combinatorial concept known as a pack. Sufficient conditions for these inequalities to be facet-defining, based on the concept of a maximal switching pack, are also provided. Moreover, we answer positively a conjecture by de Farias et~al.~about the separation complexity of the inequalities introduced in their work, and propose efficient separation algorithms for our newly defined cutting-planes.
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