.. _method-coliny_cobyla:

"""""""""""""
coliny_cobyla
"""""""""""""


Constrained Optimization BY Linear Approximations (COBYLA)



**Topics**


package_scolib, package_coliny, local_optimization_methods, constrained


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

   method-coliny_cobyla-initial_delta
   method-coliny_cobyla-variable_tolerance
   method-coliny_cobyla-solution_target
   method-coliny_cobyla-seed
   method-coliny_cobyla-show_misc_options
   method-coliny_cobyla-misc_options
   method-coliny_cobyla-max_iterations
   method-coliny_cobyla-convergence_tolerance
   method-coliny_cobyla-max_function_evaluations
   method-coliny_cobyla-scaling
   method-coliny_cobyla-model_pointer


**Specification**

- *Alias:* None

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+------------------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword               | Dakota Keyword Description                    |
|                         | Group              |                              |                                               |
+=========================+====================+==============================+===============================================+
| Optional                                     | `initial_delta`__            | Reasonable initial changes to optimization    |
|                                              |                              | variables                                     |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `variable_tolerance`__       | Required or expected accuracy in optimization |
|                                              |                              | variables.                                    |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `solution_target`__          | Stopping criteria based on objective function |
|                                              |                              | value                                         |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `seed`__                     | Seed of the random number generator           |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `show_misc_options`__        | Show algorithm parameters not exposed in      |
|                                              |                              | Dakota input                                  |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `misc_options`__             | Set method options not available through      |
|                                              |                              | Dakota spec                                   |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `max_iterations`__           | Number of iterations allowed for optimizers   |
|                                              |                              | and adaptive UQ methods                       |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `convergence_tolerance`__    | Stopping criterion based on objective         |
|                                              |                              | function or statistics convergence            |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `max_function_evaluations`__ | Number of function evaluations allowed for    |
|                                              |                              | optimizers                                    |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `scaling`__                  | Turn on scaling for variables, responses, and |
|                                              |                              | constraints                                   |
+----------------------------------------------+------------------------------+-----------------------------------------------+
| Optional                                     | `model_pointer`__            | Identifier for model block to be used by a    |
|                                              |                              | method                                        |
+----------------------------------------------+------------------------------+-----------------------------------------------+

.. __: method-coliny_cobyla-initial_delta.html
__ method-coliny_cobyla-variable_tolerance.html
__ method-coliny_cobyla-solution_target.html
__ method-coliny_cobyla-seed.html
__ method-coliny_cobyla-show_misc_options.html
__ method-coliny_cobyla-misc_options.html
__ method-coliny_cobyla-max_iterations.html
__ method-coliny_cobyla-convergence_tolerance.html
__ method-coliny_cobyla-max_function_evaluations.html
__ method-coliny_cobyla-scaling.html
__ method-coliny_cobyla-model_pointer.html



**Description**


The Constrained Optimization BY Linear Approximations (COBYLA)
algorithm is an extension to the Nelder-Mead simplex algorithm for
handling general linear/nonlinear constraints and is invoked using the
``coliny_cobyla`` group specification. The COBYLA algorithm employs
linear approximations to the objective and constraint functions, the
approximations being formed by linear interpolation at N+1 points in
the space of the variables. We regard these interpolation points as
vertices of a simplex. The step length parameter controls the size of
the simplex and it is reduced automatically from ``initial_delta`` to
``variable_tolerance``. One advantage that COBYLA has over many of its
competitors is that it treats each constraint individually when
calculating a change to the variables, instead of lumping the
constraints together into a single penalty function.

*See the page :ref:`topic-package_scolib` for important information
regarding all SCOLIB methods*

``coliny_cobyla`` is inherently serial.

*Stopping Critieria*

COBYLA currently only supports termination based on
 \li :dakkw:`method-coliny_cobyla-max_function_evaluations`
 \li :dakkw:`method-coliny_cobyla-solution_target`

Other method-independent stopping criteria ( ``max_iterations`` and
``convergence_tolerance``) will be ignored if set.

*Known Bugs*

The implementation of the ``coliny_cobyla`` optimization method is such
that the best function value is not always returned to Dakota for
reporting.  The user is advised to look through the Dakota screen
output or the tabular output file (if generated) to confirm what the
best function value and corresponding parameter values are.

The ``coliny_cobyla`` optimization method does not always respect bound
constraints when scaling is turned on.

Neither bug will be fixed, as maintaining third-party source code
(such as COBYLA) is outside of the Dakota project scope.


*Expected HDF5 Output*

If Dakota was built with HDF5 support and run with the
:dakkw:`environment-results_output-hdf5` keyword, this method
writes the following results to HDF5:


- :ref:`hdf5_results-best_params`
- :ref:`hdf5_results-best_obj_fncs` (when :dakkw:`responses-objective_functions`) are specified)
- :ref:`hdf5_results-best_constraints`
- :ref:`hdf5_results-calibration` (when :dakkw:`responses-calibration_terms` are specified)


