Blurb::
Constrained Optimization BY Linear Approximations (COBYLA)
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
\c 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 \c initial_delta to
\c 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.

<b> See the page \ref topic-package_scolib for important information
regarding all SCOLIB methods </b>

\c coliny_cobyla is inherently serial.

<b> Stopping Critieria </b>

COBYLA currently only supports termination based on
 \li \ref method-coliny_cobyla-max_function_evaluations
 \li \ref method-coliny_cobyla-solution_target

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

<b> Known Bugs </b>

The implementation of the \c 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 \c 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.


<b>Expected HDF5 Output</b> 

If Dakota was built with HDF5 support and run with the 
\ref 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 \ref responses-objective_functions) are specified) 
- \ref hdf5_results-best_constraints 
- \ref hdf5_results-calibration (when \ref responses-calibration_terms are specified) 

Topics::	package_scolib, package_coliny, local_optimization_methods, constrained
Examples::
Theory::
Faq::
See_Also::	method-coliny_beta, method-coliny_direct, method-coliny_pattern_search, method-coliny_ea, method-coliny_solis_wets
