Dantzig–Wolfe reformulations for binary quadratic problems

The purpose of this paper is to provide strong reformulations for binary quadratic problems. We propose a first methodological analysis on a family of reformulations combining Dantzig–Wolfe and Quadratic Convex optimization principles. We show that a few reformulations of our family yield continuous...

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Bibliographic Details
Published in:Mathematical programming computation Vol. 14; no. 1; pp. 85 - 120
Main Authors: Ceselli, Alberto, Létocart, Lucas, Traversi, Emiliano
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2022
Springer Nature B.V
Springer
Subjects:
Computational geometry
Computer Science
Convexity
Discrete Mathematics
Full Length Paper
Knapsack problem
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research
Operations Research/Decision Theory
Optimization
Theory of Computation
Column generation
90C11 Mixed integer programming
90C20 Quadratic programming
Decomposition methods
90C27 Combinatorial optimization
Binary quadratic programming
Quadratic convex reformulation
ISSN:1867-2949, 1867-2957
Online Access:Get full text
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Summary:The purpose of this paper is to provide strong reformulations for binary quadratic problems. We propose a first methodological analysis on a family of reformulations combining Dantzig–Wolfe and Quadratic Convex optimization principles. We show that a few reformulations of our family yield continuous relaxations that are strong in terms of dual bounds and computationally efficient to optimize. As a representative case study, we apply them to a cardinality constrained quadratic knapsack problem, providing extensive experimental insights. We report and analyze in depth a particular reformulation providing continuous relaxations whose solutions turn out to be integer optima in all our tests.
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content type line 14
ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-021-00206-w