.. _method-local_interval_est:

""""""""""""""""""
local_interval_est
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Interval analysis using local optimization



**Topics**


uncertainty_quantification, epistemic_uncertainty_quantification_methods, interval_estimation


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

   method-local_interval_est-sqp
   method-local_interval_est-nip
   method-local_interval_est-convergence_tolerance
   method-local_interval_est-model_pointer


**Specification**

- *Alias:* nond_local_interval_est 

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+---------------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword            | Dakota Keyword Description                    |
|                         | Group              |                           |                                               |
+=========================+====================+===========================+===============================================+
| Optional (Choose One)   | Optimization       | `sqp`__                   | Use a sequential quadratic programming method |
|                         | Solver             |                           | for solving an optimization sub-problem       |
|                         |                    +---------------------------+-----------------------------------------------+
|                         |                    | `nip`__                   | Use a nonlinear interior point method for     |
|                         |                    |                           | solving an optimization sub-problem           |
+-------------------------+--------------------+---------------------------+-----------------------------------------------+
| Optional                                     | `convergence_tolerance`__ | Stopping criterion based on objective         |
|                                              |                           | function or statistics convergence            |
+----------------------------------------------+---------------------------+-----------------------------------------------+
| Optional                                     | `model_pointer`__         | Identifier for model block to be used by a    |
|                                              |                           | method                                        |
+----------------------------------------------+---------------------------+-----------------------------------------------+

.. __: method-local_interval_est-sqp.html
__ method-local_interval_est-nip.html
__ method-local_interval_est-convergence_tolerance.html
__ method-local_interval_est-model_pointer.html



**Description**


Interval analysis using local methods ( ``local_interval_est``).
If the problem is amenable to local optimization
methods (e.g. can provide derivatives or use finite difference
method to calculate derivatives), then one can use one of two local
methods to calculate these bounds.

- ``sqp``
- ``nip``

*Additional Resources*

Refer to :ref:`topic-variable_support` for information on supported
variable types.



**Theory**


In interval analysis, one assumes that nothing is known about
an epistemic uncertain variable except that its value lies
somewhere within an interval. In this situation, it is NOT
assumed that the value has a uniform probability of occuring
within the interval. Instead, the interpretation is that
any value within the interval is a possible value or a potential
realization of that variable. In interval analysis, the
uncertainty quantification problem is one of determining the
resulting bounds on the output (defining the output interval)
given interval bounds on the inputs. Again, any output response
that falls within the output interval is a possible output
with no frequency information assigned to it.


