The linearization problem of a binary quadratic problem and its applications
Hu,Hao Sotirov,Renata
Hu,Hao
Sotirov,Renata
Abstract
We provide several applications of the linearization problem of a binary quadratic problem. We propose a new lower bounding strategy, called the linearization-based scheme, that is based on a simple certificate for a quadratic function to be non-negative on the feasible set. Each linearization-based bound requires a set of linearizable matrices as an input. We prove that the Generalized Gilmore-Lawler bounding scheme for binary quadratic problems provides linearization-based bounds. Moreover, we show that the bound obtained from the first level reformulation linearization technique is also a type of linearization-based bound, which enables us to provide a comparison among mentioned bounds. However, the strongest linearization-based bound is the one that uses the full characterization of the set of linearizable matrices. Finally, we present a polynomial-time algorithm for the linearization problem of the quadratic shortest path problem on directed acyclic graphs. Our algorithm gives a complete characterization of the set of linearizable matrices for the quadratic shortest path problem.
Description
Date
2021-12
Journal Title
Journal ISSN
Volume Title
Publisher
Research Projects
Organizational Units
Journal Issue
Keywords
Binary quadratic program, Generalized Gilmore–Lawler bound, Linearization problem, Quadratic assignment problem, Quadratic shortest path problem
Citation
Hu, H & Sotirov, R 2021, 'The linearization problem of a binary quadratic problem and its applications', Annals of Operations Research, vol. 307, no. 1-2, pp. 229-249. https://doi.org/10.1007/s10479-021-04310-x
License
info:eu-repo/semantics/openAccess