Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: Part II

This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products where both variables are bou...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 87; no. 3; pp. 893 - 934
Main Authors: Beach, Benjamin, Burlacu, Robert, Bärmann, Andreas, Hager, Lukas, Hildebrand, Robert
Format: Journal Article
Language:English
Published: New York, NY Springer US 01.04.2024
Springer Nature B.V
Subjects:
Binarization
Continuity (mathematics)
Convex and Discrete Geometry
Discretization
Integer programming
Linear programming
Management Science
Mathematics
Mathematics and Statistics
MIP Relaxations
Mixed integer
Operations Research
Operations Research/Decision Theory
Optimization
Piecewise linear approximation
Quadratic programming
Statistics
Variables
Binarization
Discretization
Quadratic programming
Piecewise linear approximation
MIP Relaxations
ISSN:1573-2894, 0926-6003, 1573-2894
Online Access:Get full text
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Summary:This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products where both variables are bounded and extend the well-known MIP relaxation normalized multiparametric disaggregation technique (NMDT), applying a sophisticated discretization to both variables. We refer to this approach as doubly discretized normalized multiparametric disaggregation technique (D-NMDT). In a comprehensive theoretical analysis, we underline the theoretical advantages of the enhanced method D-NMDT compared to NMDT. Furthermore, we perform a broad computational study to demonstrate its effectiveness in terms of producing tight dual bounds for MIQCQPs. Finally, we compare D-NMDT to the separable MIP relaxations from Part I and a state-of-the-art MIQCQP solver.
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ISSN:1573-2894
0926-6003
1573-2894
DOI:10.1007/s10589-024-00554-y