# Dynamically generated cutting planes for mixed-integer quadratically constrained quadratic programs and their incorporation into GloMIQO 2

## Author(s): Misener, Ruth; Smadbeck, James B; Floudas, Christodoulos A

To refer to this page use: http://arks.princeton.edu/ark:/88435/pr14v99
DC FieldValueLanguage
dc.contributor.authorMisener, Ruth-
dc.contributor.authorFloudas, Christodoulos A-
dc.date.accessioned2021-10-08T19:58:47Z-
dc.date.available2021-10-08T19:58:47Z-
dc.date.issued2015en_US
dc.identifier.citationMisener, Ruth, James B. Smadbeck, and Christodoulos A. Floudas. "Dynamically generated cutting planes for mixed-integer quadratically constrained quadratic programs and their incorporation into GloMIQO 2." Optimization Methods and Software 30, no. 1 (2015): 215-249. doi: 10.1080/10556788.2014.916287en_US
dc.identifier.issn1055-6788-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr14v99-
dc.description.abstractThe global mixed-integer quadratic optimizer, GloMIQO, addresses mixed-integer quadratically constrained quadratic programs (MIQCQP) to ε-global optimality. This paper documents the branch-and-cut framework integrated into GloMIQO 2. Cutting planes are derived from reformulation–linearization technique equations, convex multivariable terms, αBB convexifications, and low- and high-dimensional edge-concave aggregations. Cuts are based on both individual equations and collections of nonlinear terms in MIQCQP. Novel contributions of this paper include: development of a corollary to Crama's [Concave extensions for nonlinear 0-1 maximization problems, Math. Program. 61 (1993), pp. 53–60] necessary and sufficient condition for the existence of a cut dominating the termwise relaxation of a bilinear expression; algorithmic descriptions for deriving each class of cut; presentation of a branch-and-cut framework integrating the cuts. Computational results are presented along with comparison of the GloMIQO 2 performance to several state-of-the-art solvers.en_US
dc.format.extent215 - 249en_US
dc.language.isoen_USen_US
dc.relation.ispartofOptimization Methods and Softwareen_US
dc.rightsAuthor's manuscripten_US
dc.titleDynamically generated cutting planes for mixed-integer quadratically constrained quadratic programs and their incorporation into GloMIQO 2en_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1080/10556788.2014.916287-
dc.identifier.eissn1029-4937-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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