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Maximal Quadratic-Free Sets
- Source :
- Integer Programming and Combinatorial Optimization ISBN: 9783030457709, IPCO
- Publication Year :
- 2020
- Publisher :
- Springer International Publishing, 2020.
-
Abstract
- 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.
- Subjects :
- Quadratic growth
Vertex (graph theory)
050101 languages & linguistics
Intersection (set theory)
05 social sciences
02 engineering and technology
Combinatorics
Linear inequality
Quadratic equation
Conic section
0202 electrical engineering, electronic engineering, information engineering
020201 artificial intelligence & image processing
0501 psychology and cognitive sciences
Quadratic programming
Cutting-plane method
Mathematics
Subjects
Details
- ISBN :
- 978-3-030-45770-9
- ISBNs :
- 9783030457709
- Database :
- OpenAIRE
- Journal :
- Integer Programming and Combinatorial Optimization ISBN: 9783030457709, IPCO
- Accession number :
- edsair.doi...........4effa046f791f309773f890eb14f2ac4