.. _method-surrogate_based_local-approx_subproblem-augmented_lagrangian_objective:

""""""""""""""""""""""""""""""
augmented_lagrangian_objective
""""""""""""""""""""""""""""""


Augmented Lagrangian approximate subproblem formulation


.. toctree::
   :hidden:
   :maxdepth: 1



**Specification**

- *Alias:* None

- *Arguments:* None


**Description**


For SBL problems with nonlinear constraints, a number of algorithm
formulations exist as described in :cite:p:`Eld06b`
and as summarized in :ref:`adv_meth:sbm:sblm`.
First, the "primary" functions (that is, the objective
functions or calibration terms) in the approximate subproblem can be
selected to be surrogates of the original primary functions (
``original_primary``), a single objective function ( ``,single_objective``)
formed from the primary function surrogates, or either an augmented
Lagrangian merit function ( ``augmented_lagrangian_objective``) or a
Lagrangian merit function ( ``lagrangian_objective``) formed from the
primary and secondary function surrogates.  The former option may
imply the use of a nonlinear least squares method, a multiobjective
optimization method, or a single objective optimization method to
solve the approximate subproblem, depending on the definition of the
primary functions.  The latter three options all imply the use of a
single objective optimization method regardless of primary function
definition.