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

The 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 techni...

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Bibliographic Details
Published in:Optimization methods & software Vol. 30; no. 1; pp. 215 - 249
Main Authors: Misener, Ruth, Smadbeck, James B., Floudas, Christodoulos A.
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.01.2015
Taylor & Francis Ltd
Subjects:
Constraints
Cutting
cutting planes
global optimization
Integer programming
Mathematical analysis
Maximization
Nonlinearity
Optimization
Planes
quadratically constrained quadratic programming
Solvers
ISSN:1055-6788, 1029-4937
Online Access:Get full text
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Summary:The 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.
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ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2014.916287