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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Published in:Discrete optimization Vol. 24; pp. 3 - 31
Main Authors: Belotti, Pietro, Góez, Julio C., Pólik, Imre, Ralphs, Ted K., Terlaky, Tamás
Format: Journal Article
Language:English
Published: Elsevier B.V 01.05.2017
Subjects:
Disjunctive conic cuts
Disjunctive programming
Mixed integer optimization
Second order cone optimization
Second order cone optimization
Mixed integer optimization
Disjunctive programming
Disjunctive conic cuts
ISSN:1572-5286, 1873-636X
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Abstract 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.
AbstractList 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.
Author Pólik, Imre
Góez, Julio C.
Ralphs, Ted K.
Belotti, Pietro
Terlaky, Tamás
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  email: terlaky@lehigh.edu
  organization: Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, 18015, USA
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Cites_doi 10.1090/S0002-9904-1958-10224-4
10.1007/s10107-006-0086-0
10.1016/S0167-5060(08)70342-X
10.1007/s101070050103
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Keywords Second order cone optimization
Mixed integer optimization
Disjunctive programming
Disjunctive conic cuts
Language English
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SubjectTerms Disjunctive conic cuts
Disjunctive programming
Mixed integer optimization
Second order cone optimization
Title A complete characterization of disjunctive conic cuts for mixed integer second order cone optimization
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