.. _method-surrogate_based_local-approx_subproblem:

"""""""""""""""""
approx_subproblem
"""""""""""""""""


Identify functions to be included in surrogate merit function


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

   method-surrogate_based_local-approx_subproblem-original_primary
   method-surrogate_based_local-approx_subproblem-single_objective
   method-surrogate_based_local-approx_subproblem-augmented_lagrangian_objective
   method-surrogate_based_local-approx_subproblem-lagrangian_objective
   method-surrogate_based_local-approx_subproblem-original_constraints
   method-surrogate_based_local-approx_subproblem-linearized_constraints
   method-surrogate_based_local-approx_subproblem-no_constraints


**Specification**

- *Alias:* None

- *Arguments:* None

- *Default:* original_primary original_constraints


**Child Keywords:**

+-------------------------+--------------------+------------------------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword                     | Dakota Keyword Description                    |
|                         | Group              |                                    |                                               |
+=========================+====================+====================================+===============================================+
| Required (Choose One)   | Objective          | `original_primary`__               | Construct approximations of all primary       |
|                         | Formulation        |                                    | functions                                     |
|                         |                    +------------------------------------+-----------------------------------------------+
|                         |                    | `single_objective`__               | Construct approximation a single objective    |
|                         |                    |                                    | functions only                                |
|                         |                    +------------------------------------+-----------------------------------------------+
|                         |                    | `augmented_lagrangian_objective`__ | Augmented Lagrangian approximate subproblem   |
|                         |                    |                                    | formulation                                   |
|                         |                    +------------------------------------+-----------------------------------------------+
|                         |                    | `lagrangian_objective`__           | Lagrangian approximate subproblem formulation |
+-------------------------+--------------------+------------------------------------+-----------------------------------------------+
| Required (Choose One)   | Constraint         | `original_constraints`__           | Use the constraints directly                  |
|                         | Formulation        +------------------------------------+-----------------------------------------------+
|                         |                    | `linearized_constraints`__         | Use linearized approximations to the          |
|                         |                    |                                    | constraints                                   |
|                         |                    +------------------------------------+-----------------------------------------------+
|                         |                    | `no_constraints`__                 | Don't use constraints                         |
+-------------------------+--------------------+------------------------------------+-----------------------------------------------+

.. __: method-surrogate_based_local-approx_subproblem-original_primary.html
__ method-surrogate_based_local-approx_subproblem-single_objective.html
__ method-surrogate_based_local-approx_subproblem-augmented_lagrangian_objective.html
__ method-surrogate_based_local-approx_subproblem-lagrangian_objective.html
__ method-surrogate_based_local-approx_subproblem-original_constraints.html
__ method-surrogate_based_local-approx_subproblem-linearized_constraints.html
__ method-surrogate_based_local-approx_subproblem-no_constraints.html



**Description**


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. Second, the surrogate constraints in the approximate
subproblem can be selected to be surrogates of the original
constraints ( ``original_constraints``) or linearized approximations to
the surrogate constraints ( ``linearized_constraints``), or constraints
can be omitted from the subproblem ( ``no_constraints``).


