7692
eng
reportzib
0
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2019-11-29
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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.
1438-0064
urn:nbn:de:0297-zib-76922
Felipe Serrano
Felipe Serrano
Gonzalo MuĂ±oz
ZIB-Report
19-56
eng
uncontrolled
MINLP
eng
uncontrolled
Quadratic Optimization
deu
uncontrolled
Cutting planes
OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
Mathematical Optimization
Serrano, Felipe
MIP-ZIBOPT
MODAL-SynLab
MODAL-Gesamt
EnBA-M
https://opus4.kobv.de/opus4-zib/files/7692/possible_structure.pdf