Enhancing the normalized multiparametric disaggregation technique for mixed-integer quadratic programming

We propose methods for improving the relaxations obtained by the normalized multiparametric disaggregation technique (NMDT). These relaxations constitute a key component for some methods for solving nonconvex mixed-integer quadratically constrained quadratic programming (MIQCQP) problems. It is show...

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Bibliographic Details
Published in:Journal of global optimization Vol. 73; no. 4; pp. 701 - 722
Main Authors: Andrade, Tiago, Oliveira, Fabricio, Hamacher, Silvio, Eberhard, Andrew
Format: Journal Article
Language:English
Published: New York Springer US 15.04.2019
Springer
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Mathematics
Mathematics and Statistics
Methods
Operations Research/Decision Theory
Optimization
Quadratic programming
Real Functions
McCormick envelopes
Convex relaxation
Nonconvex mixed-integer quadratically constrained quadratic programs
Normalized multiparametric disaggregation technique
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:We propose methods for improving the relaxations obtained by the normalized multiparametric disaggregation technique (NMDT). These relaxations constitute a key component for some methods for solving nonconvex mixed-integer quadratically constrained quadratic programming (MIQCQP) problems. It is shown that these relaxations can be more efficiently formulated by significantly reducing the number of auxiliary variables (in particular, binary variables) and constraints. Moreover, a novel algorithm for solving MIQCQP problems is proposed. It can be applied using either its original NMDT or the proposed reformulation. Computational experiments are performed using both benchmark instances from the literature and randomly generated instances. The numerical results suggest that the proposed techniques can improve the quality of the relaxations.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-018-0728-9