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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Vydané v:Mathematical programming computation Ročník 14; číslo 1; s. 85 - 120
Hlavní autori: Ceselli, Alberto, Létocart, Lucas, Traversi, Emiliano
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2022
Springer Nature B.V
Springer
Predmet:
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
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Abstract 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.
AbstractList 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.
Author Ceselli, Alberto
Traversi, Emiliano
Létocart, Lucas
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  surname: Ceselli
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  givenname: Emiliano
  surname: Traversi
  fullname: Traversi, Emiliano
  organization: LIPN, CNRS, (UMR 7030), Université Sorbonne Paris Nord
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Issue 1
Keywords Column generation
90C11 Mixed integer programming
90C20 Quadratic programming
Decomposition methods
90C27 Combinatorial optimization
Binary quadratic programming
Quadratic convex reformulation
Language English
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Snippet The purpose of this paper is to provide strong reformulations for binary quadratic problems. We propose a first methodological analysis on a family of...
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SubjectTerms 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
Title Dantzig–Wolfe reformulations for binary quadratic problems
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https://www.proquest.com/docview/2637579375
https://hal.science/hal-03554329
Volume 14
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