Dakota Reference Manual: coliny_cobyla

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coliny_cobyla

Constrained Optimization BY Linear Approximations (COBYLA)

## Topics

This keyword is related to the topics:

- package_scolib
- package_coliny
- local_optimization_methods
- constrained

## Specification

Alias: none

Argument(s): none

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| 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

## 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 package_scolib for important information regarding all SCOLIB methods

`coliny_cobyla` is inherently serial.

Stopping Critieria

COBYLA currently only supports termination based on

- max_function_evaluations
- 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 hdf5 keyword, this method writes the following results to HDF5:

- Best Parameters
- Best Objective Functions (when objective_functions) are specified)
- Best Nonlinear Constraints
- Calibration (when calibration_terms are specified)

## See Also

These keywords may also be of interest:

- coliny_beta
- coliny_direct
- coliny_pattern_search
- coliny_ea
- coliny_solis_wets