.. _responses-mixed_hessians:

""""""""""""""
mixed_hessians
""""""""""""""


Hessians are needed and will be obtained from a mix of numerical,
analytic, and "quasi" sources


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

   responses-mixed_hessians-id_numerical_hessians
   responses-mixed_hessians-relative
   responses-mixed_hessians-absolute
   responses-mixed_hessians-bounds
   responses-mixed_hessians-forward
   responses-mixed_hessians-central
   responses-mixed_hessians-id_quasi_hessians
   responses-mixed_hessians-id_analytic_hessians


**Specification**

- *Alias:* None

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+---------------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword            | Dakota Keyword Description                    |
|                         | Group              |                           |                                               |
+=========================+====================+===========================+===============================================+
| Optional                                     | `id_numerical_hessians`__ | Identify which numerical-Hessian corresponds  |
|                                              |                           | to which response                             |
+-------------------------+--------------------+---------------------------+-----------------------------------------------+
| Optional (Choose One)   | Step Scaling       | `relative`__              | (Default) Scale step size by the parameter    |
|                         |                    |                           | value                                         |
|                         |                    +---------------------------+-----------------------------------------------+
|                         |                    | `absolute`__              | Do not scale step-size                        |
|                         |                    +---------------------------+-----------------------------------------------+
|                         |                    | `bounds`__                | Scale step-size by the domain of the          |
|                         |                    |                           | parameter                                     |
+-------------------------+--------------------+---------------------------+-----------------------------------------------+
| Optional (Choose One)   | Finite Difference  | `forward`__               | (Default) Use forward differences             |
|                         | Type               +---------------------------+-----------------------------------------------+
|                         |                    | `central`__               | Use central differences                       |
+-------------------------+--------------------+---------------------------+-----------------------------------------------+
| Optional                                     | `id_quasi_hessians`__     | Identify which quasi-Hessian corresponds to   |
|                                              |                           | which response                                |
+----------------------------------------------+---------------------------+-----------------------------------------------+
| Optional                                     | `id_analytic_hessians`__  | Identify which analytical Hessian corresponds |
|                                              |                           | to which response                             |
+----------------------------------------------+---------------------------+-----------------------------------------------+

.. __: responses-mixed_hessians-id_numerical_hessians.html
__ responses-mixed_hessians-relative.html
__ responses-mixed_hessians-absolute.html
__ responses-mixed_hessians-bounds.html
__ responses-mixed_hessians-forward.html
__ responses-mixed_hessians-central.html
__ responses-mixed_hessians-id_quasi_hessians.html
__ responses-mixed_hessians-id_analytic_hessians.html



**Description**


The ``mixed_hessians`` specification means that some Hessian
information is available directly from the simulation (analytic)
whereas the rest will have to be estimated by finite differences
(numerical) or approximated by secant updating. As for
mixed gradients, this specification allows the user to make use of as
much analytic information as is available and then
estimate/approximate the rest.

The ``id_analytic_hessians`` list
specifies by number the functions which have analytic Hessians, and
the ``id_numerical_hessians`` and ``id_quasi_hessians`` lists specify by
number the functions which must use numerical Hessians and
secant Hessian updates, respectively. Each function identifier,
from 1 through the total number of functions, must appear once and
only once within the union of the ``id_analytic_hessians``,
``id_numerical_hessians``, and ``id_quasi_hessians`` lists.

The
``fd_hessian_step_size`` and ``bfgs``, ``damped`` ``bfgs``, or ``sr1``
secant update selections are as described previously in
:dakkw:`responses` and pertain to those functions
listed by the ``id_numerical_hessians`` and ``id_quasi_hessians``
lists.


