Practical Augmented Lagrangian Methods

  title={Practical Augmented Lagrangian Methods},
  author={Ernesto G. Birgin and Jos{\'e} Mario Mart{\'i}nez},
  booktitle={Encyclopedia of Optimization},
for all x ∈ IR, λ ∈ IR, μ ∈ IR +. PHR-based Augmented Lagrangian methods for solving (1) are based on the iterative (approximate) minimization of Lρ with respect to x ∈ Ω, followed by the updating of the penalty parameter ρ and the Lagrange multipliers approximations λ and μ. The most popular practical Augmented Lagrangian method gave rise to the Lancelot package [24, 25, 26]. Lancelot does not use inequality constraints g(x) ≤ 0 in its problem formulation. When an inequality 

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