.. _method-surrogate_based_local-merit_function:

""""""""""""""
merit_function
""""""""""""""


Select type of penalty or merit function


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

   method-surrogate_based_local-merit_function-penalty_merit
   method-surrogate_based_local-merit_function-adaptive_penalty_merit
   method-surrogate_based_local-merit_function-lagrangian_merit
   method-surrogate_based_local-merit_function-augmented_lagrangian_merit


**Specification**

- *Alias:* None

- *Arguments:* None

- *Default:* augmented_lagrangian_merit


**Child Keywords:**

+-------------------------+--------------------+--------------------------------+---------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword                 | Dakota Keyword Description                  |
|                         | Group              |                                |                                             |
+=========================+====================+================================+=============================================+
| Required (Choose One)   | Merit Function     | `penalty_merit`__              | Use penalty merit function                  |
|                         |                    +--------------------------------+---------------------------------------------+
|                         |                    | `adaptive_penalty_merit`__     | Use adaptive penalty merit function         |
|                         |                    +--------------------------------+---------------------------------------------+
|                         |                    | `lagrangian_merit`__           | Use first-order Lagrangian merit function   |
|                         |                    +--------------------------------+---------------------------------------------+
|                         |                    | `augmented_lagrangian_merit`__ | Use combined penalty and zeroth-order       |
|                         |                    |                                | Lagrangian merit function                   |
+-------------------------+--------------------+--------------------------------+---------------------------------------------+

.. __: method-surrogate_based_local-merit_function-penalty_merit.html
__ method-surrogate_based_local-merit_function-adaptive_penalty_merit.html
__ method-surrogate_based_local-merit_function-lagrangian_merit.html
__ method-surrogate_based_local-merit_function-augmented_lagrangian_merit.html



**Description**


Following optimization of the approximate subproblem, the candidate
iterate is evaluated using a merit function, which can be selected to
be a simple penalty function with penalty ramped by
surrogate_based_local iteration number ( ``penalty_merit``), an adaptive
penalty function where the penalty ramping may be accelerated in order
to avoid rejecting good iterates which decrease the constraint
violation ( ``adaptive_penalty_merit``), a Lagrangian merit function
which employs first-order Lagrange multiplier updates (
``lagrangian_merit``), or an augmented Lagrangian merit function which
employs both a penalty parameter and zeroth-order Lagrange multiplier
updates ( ``augmented_lagrangian_merit``). When an augmented Lagrangian
is selected for either the subproblem objective or the merit function
(or both), updating of penalties and multipliers follows the approach
described in :cite:p:`Con00`.