A complete characterization of disjunctive conic cuts for mixed integer second order cone optimization

We study the convex hull of the intersection of a disjunctive set defined by parallel hyperplanes and the feasible set of a mixed integer second order cone optimization (MISOCO) problem. We extend our prior work on disjunctive conic cuts (DCCs), which has thus far been restricted to the case in whic...

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Bibliographic Details
Published in:Discrete optimization 2017-05, Vol.24, p.3-31
Main Authors: Belotti, Pietro, Góez, Julio C., Pólik, Imre, Ralphs, Ted K., Terlaky, Tamás
Format: Article
Language:English
Subjects:
Disjunctive conic cuts
Disjunctive programming
Mixed integer optimization
Second order cone optimization
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Summary:We study the convex hull of the intersection of a disjunctive set defined by parallel hyperplanes and the feasible set of a mixed integer second order cone optimization (MISOCO) problem. We extend our prior work on disjunctive conic cuts (DCCs), which has thus far been restricted to the case in which the intersection of the hyperplanes and the feasible set is bounded. Using a similar technique, we show that one can extend our previous results to the case in which that intersection is unbounded. We provide a complete characterization in closed form of the conic inequalities required to describe the convex hull when the hyperplanes defining the disjunction are parallel.
ISSN:1572-5286
1873-636X
DOI:10.1016/j.disopt.2016.10.001