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

We study mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We present MIP relaxation methods for non-convex continuous variable products. In this paper, we consider MIP relaxations based on separ...

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Vydané v:Computational optimization and applications Ročník 87; číslo 3; s. 835 - 891
Hlavní autori: Beach, Benjamin, Burlacu, Robert, Bärmann, Andreas, Hager, Lukas, Hildebrand, Robert
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York, NY Springer US 01.04.2024
Springer Nature B.V
Predmet:
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
Binarization
Discretization
Quadratic programming
Piecewise linear approximation
MIP relaxations
ISSN:1573-2894, 0926-6003, 1573-2894
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Shrnutí:We study mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We present MIP relaxation methods for non-convex continuous variable products. In this paper, we consider MIP relaxations based on separable reformulation. The main focus is the introduction of the enhanced separable MIP relaxation for non-convex quadratic products of the form z=xy, called hybrid separable (HybS). Additionally, we introduce a logarithmic MIP relaxation for univariate quadratic terms, called sawtooth relaxation , based on Beach (Beach in J Glob Optim 84:869–912, 2022). We combine the latter with HybS and existing separable reformulations to derive MIP relaxations of MIQCQPs. We provide a comprehensive theoretical analysis of these techniques, underlining the theoretical advantages of HybS compared to its predecessors. We perform a broad computational study to demonstrate the effectiveness of the enhanced MIP relaxation in terms of producing tight dual bounds for MIQCQPs. In Part II, we study MIP relaxations that extend the MIP relaxation normalized multiparametric disaggregation technique (NMDT) (Castro in J Glob Optim 64:765–784, 2015) and present a computational study which also includes the MIP relaxations from this work and compares them with a state-of-the-art of MIQCQP solvers.
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ISSN:1573-2894
0926-6003
1573-2894
DOI:10.1007/s10589-023-00543-7