Maximal Quadratic-Free Sets
Please always quote using this URN: urn:nbn:de:0297-zib-76922
- 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: | ZIB-Report |
| Tag: | Cutting planes MINLP; Quadratic Optimization |
| MSC-Classification: | 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING |
| Date of first Publication: | 2019/11/29 |
| Series (Serial Number): | ZIB-Report (19-56) |
| ISSN: | 1438-0064 |
