Augmented Lagrangian Methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they replace a constrained optimization problem by a series of unconstrained problems; the difference is that the augmented Lagrangian method adds an additional term to the unconstrained objective. This additional term is designed to mimic a Lagrange multiplier. The augmented Lagrangian is not the same as the method of Lagrange multipliers. Viewed differently, the unconstrained objective is the Lagrangian of the constrained problem, with an additional penalty term (the augmentation). … Augmented Lagrangian Method google