Augmented Lagrangian
algorithms are based on successive minimization of the
augmented Lagrangian 
with
respect to 
, with updates of 
and possibly 
occurring between iterations. An augmented Lagrangian
algorithm for the constrained optimization problem computes 
as an approximate minimizer of the subproblem
where
includes only the equality constraints. Updating of the multipliers
usually takes the form
This approach is relatively easy to implement because the main
computational operation at each iteration is minimization of the smooth function with respect
to , subject
only to bound constraints. A large-scale implementation of the augmented Lagrangian
approach can be found in the LANCELOT
package, which solves the bound-constrained subproblem by using special data
structures to exploit the (group partially separable) structure of the underlying problem.
The OPTIMA and OPTPACK libraries also contain
augmented Lagrangian codes.
Up To:
Nonlinearly Constrained Optimization.
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Updated 28 March 1996
