.. _method-approximate_control_variate-solution_mode-online_pilot-relaxation:

""""""""""
relaxation
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For an online pilot mode, apply under-relaxation to the shared sample increments



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

   method-approximate_control_variate-solution_mode-online_pilot-relaxation-factor_sequence
   method-approximate_control_variate-solution_mode-online_pilot-relaxation-fixed_factor
   method-approximate_control_variate-solution_mode-online_pilot-relaxation-recursive_factor


**Specification**

- *Alias:* None

- *Arguments:* None

- *Default:* no relaxation


**Child Keywords:**

+-------------------------+--------------------+----------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword       | Dakota Keyword Description                    |
|                         | Group              |                      |                                               |
+=========================+====================+======================+===============================================+
| Required (Choose One)   | Relaxation factor  | `factor_sequence`__  | For under-relaxation of shared sample         |
|                         |                    |                      | increments, apply a sequence of factors, one  |
|                         |                    |                      | per iteration                                 |
|                         |                    +----------------------+-----------------------------------------------+
|                         |                    | `fixed_factor`__     | For under-relaxation of shared sample         |
|                         |                    |                      | increments, apply a fixed factor that is      |
|                         |                    |                      | invariant with iteration                      |
|                         |                    +----------------------+-----------------------------------------------+
|                         |                    | `recursive_factor`__ | For under-relaxation of shared sample         |
|                         |                    |                      | increments, apply a recursive factor on each  |
|                         |                    |                      | iteration that advances the relaxation factor |
|                         |                    |                      | toward 1                                      |
+-------------------------+--------------------+----------------------+-----------------------------------------------+

.. __: method-approximate_control_variate-solution_mode-online_pilot-relaxation-factor_sequence.html
__ method-approximate_control_variate-solution_mode-online_pilot-relaxation-fixed_factor.html
__ method-approximate_control_variate-solution_mode-online_pilot-relaxation-recursive_factor.html



**Description**


Multilevel / multifidelity sampling methods are adaptive UQ methods
that utilize a pilot sample to estimate an initial set of correlations
or variances, and then augment the pilot with additional sample
increments to optimally allocate resources.  In the iterated
``online_pilot`` solution mode, the initial pilot sample is updated with
additional shared samples in the direction of the optimal solution to
the resource allocation problem.  When the initial correlation /
covariance approximations are inaccurate, this update can be overly
aggressive, such that it becomes advisable to only accept a portion of
this suggested increment through use of an under-relaxation factor.

Three options are provided for defining a sequence of under-relaxation
factors: ``factor_sequence``, ``fixed_factor``, and ``recursive_factor``.

**Default Behavior**

Relaxation is an optional specification, and no relaxation (accept the
full magnitude of suggested sample increments) is the default.