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In the field of mathematical optimization, Lagrangian relaxation is a relaxation method which approximates a difficult problem of constrained optimization by a simpler problem. A solution to the relaxed problem is an approximate solution to the original problem, and provides useful information. The problem of maximizing the Lagrangian function of the dual variables (the Lagrangian multipliers) is the Lagrangian dual problem.

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  • Relaxation lagrangienne (fr)
  • Lagrangian relaxation (en)
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  • La relaxation lagrangienne est une technique de relaxation qui consiste à supprimer des contraintes difficiles en les intégrant dans la fonction objectif en la pénalisant si ces contraintes ne sont pas respectées. (fr)
  • In the field of mathematical optimization, Lagrangian relaxation is a relaxation method which approximates a difficult problem of constrained optimization by a simpler problem. A solution to the relaxed problem is an approximate solution to the original problem, and provides useful information. The problem of maximizing the Lagrangian function of the dual variables (the Lagrangian multipliers) is the Lagrangian dual problem. (en)
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  • La relaxation lagrangienne est une technique de relaxation qui consiste à supprimer des contraintes difficiles en les intégrant dans la fonction objectif en la pénalisant si ces contraintes ne sont pas respectées. (fr)
  • In the field of mathematical optimization, Lagrangian relaxation is a relaxation method which approximates a difficult problem of constrained optimization by a simpler problem. A solution to the relaxed problem is an approximate solution to the original problem, and provides useful information. The method penalizes violations of inequality constraints using a Lagrange multiplier, which imposes a cost on violations. These added costs are used instead of the strict inequality constraints in the optimization. In practice, this relaxed problem can often be solved more easily than the original problem. The problem of maximizing the Lagrangian function of the dual variables (the Lagrangian multipliers) is the Lagrangian dual problem. (en)
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