Best reduction of the quadratic semi-assignment problem

We consider the quadratic semi-assignment problem in which we minimize a quadratic pseudo-Boolean function F subject to the semi-assignment constraints. We propose in this paper a linear programming method to obtain the best reduction of this problem, i.e. to compute the greatest constant c such tha...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 109; no. 3; pp. 197 - 213
Main Authors: Billionnet, Alain, Elloumi, Sourour
Format: Journal Article
Language:English
Published: Lausanne Elsevier B.V 2001
Amsterdam Elsevier
New York, NY
Subjects:
0–1 quadratic programming
Applied sciences
Calculus of variations and optimal control
Computational Complexity
Computer Science
Exact sciences and technology
Linear programming
Mathematical analysis
Mathematical programming
Mathematics
Operational research and scientific management
Operational research. Management science
Reduction
Roof duality
Sciences and techniques of general use
Semi-assignment problem
Linear programming
Reduction
Semi-assignment problem
Roof duality
0–1 quadratic programming
Boolean function
Duality
Distributed system
Quadratic programming
Constrained optimization
Quasi semi assignement problem
Lagrange multiplier
Allocation
Optimal solution
Feasible direction method
NP hard problem
Quadratic pseudo Boolean function
Problem reduction
Mathematical programming
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary:We consider the quadratic semi-assignment problem in which we minimize a quadratic pseudo-Boolean function F subject to the semi-assignment constraints. We propose in this paper a linear programming method to obtain the best reduction of this problem, i.e. to compute the greatest constant c such that F is equal to c plus F′ for all feasible solutions, F′ being a quadratic pseudo-Boolean function with nonnegative coefficients. Thus constant c can be viewed as a generalization of the height of an unconstrained quadratic 0–1 function introduced in (Hammer et al., Math. Program. 28 (1984) 121–155), to constrained quadratic 0–1 optimization. Finally, computational experiments proving the practical usefulness of this reduction are reported.
ISSN:0166-218X
1872-6771
DOI:10.1016/S0166-218X(00)00257-2