New Classes of Facets for Complementarity Knapsack Problems
Optimization and Control
2022-12-29 v3
Abstract
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.
Cite
@article{arxiv.2203.02873,
title = {New Classes of Facets for Complementarity Knapsack Problems},
author = {Alberto Del Pia and Jeff Linderoth and Haoran Zhu},
journal= {arXiv preprint arXiv:2203.02873},
year = {2022}
}