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

Benjamin Beach (), Robert Burlacu (), Andreas Bärmann (), Lukas Hager () and Robert Hildebrand ()
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Benjamin Beach: Virginia Tech
Robert Burlacu: Fraunhofer Institute for Integrated Circuits IIS
Andreas Bärmann: Friedrich-Alexander-Universität Erlangen-Nürnberg
Lukas Hager: Friedrich-Alexander-Universität Erlangen-Nürnberg
Robert Hildebrand: Virginia Tech

Computational Optimization and Applications, 2024, vol. 87, issue 3, No 8, 893-934

Abstract: Abstract 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.

Keywords: Quadratic programming; MIP Relaxations; Discretization; Binarization; Piecewise linear approximation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-024-00554-y

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