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2004•Archive ouverte UNIGE (University of Geneva)Open access

Semi-Lagrangian Relaxation

C. Beltran‐Royo, Claude Tadonki, Jean-Philippe Vial

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Abstract

Lagrangian relaxation is commonly used in combinatorial optimization to generate lower bounds for a minimization problem. We propose a modified Lagrangian relaxation which used in (linear) combinatorial optimization with equality constraints generates an optimal intinteger solution. We call this new concept semi-Lagrangian relaxation and illustrate its practical value by solving large-scale instances of the p-median problem.

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Lagrangian relaxation is commonly used in combinatorial optimization to generate lower bounds for a minimization problem. We propose a modified Lagrangian relaxation which used in (linear) combinatorial optimization with equality constraints generates an optimal intinteger solution. We call this new concept semi-Lagrangian relaxation and illustrate its practical value by solving large-scale instances of the p-median problem.

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Available abstract

Lagrangian relaxation is commonly used in combinatorial optimization to generate lower bounds for a minimization problem. We propose a modified Lagrangian relaxation which used in (linear) combinatorial optimization with equality constraints generates an optimal intinteger solution. We call this new concept semi-Lagrangian relaxation and illustrate its practical value by solving large-scale instances of the p-median problem.

Key concepts: Lagrangian relaxation, Lagrangian, Relaxation (psychology), Minification, Mathematical optimization, Mathematics, Combinatorial optimization, Optimization problem

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