Maximal Quadratic-Free Sets
- The intersection cut paradigm is a powerful framework that facilitates the generation of valid linear inequalities, or cutting planes, for a potentially complex set S. The key ingredients in this construction are a simplicial conic relaxation of S and an S-free set: a convex zone whose interior does not intersect S. Ideally, such S-free set would be maximal inclusion-wise, as it would generate a deeper cutting plane. However, maximality can be a challenging goal in general. In this work, we show how to construct maximal S-free sets when S is defined as a general quadratic inequality. Our maximal S-free sets are such that efficient separation of a vertex in LP-based approaches to quadratically constrained problems is guaranteed. To the best of our knowledge, this work is the first to provide maximal quadratic-free sets.
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| Author: | Felipe SerranoORCiD, Gonzalo MuñozORCiD |
|---|---|
| Document Type: | In Proceedings |
| Parent Title (English): | Integer Programming and Combinatorial Optimization: 21th International Conference, IPCO 2020 |
| First Page: | 307 |
| Last Page: | 321 |
| Year of first publication: | 2020 |
| Preprint: | urn:nbn:de:0297-zib-76922 |
| DOI: | https://doi.org/10.1007/978-3-030-45771-6_24 |
