.. _method:

""""""
method
""""""


Begins Dakota method selection and behavioral settings.



**Topics**


block


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

   method-id_method
   method-output
   method-final_solutions
   method-hybrid
   method-multi_start
   method-pareto_set
   method-branch_and_bound
   method-surrogate_based_local
   method-surrogate_based_global
   method-dot_frcg
   method-dot_mmfd
   method-dot_bfgs
   method-dot_slp
   method-dot_sqp
   method-conmin_frcg
   method-conmin_mfd
   method-dl_solver
   method-npsol_sqp
   method-nlssol_sqp
   method-nlpql_sqp
   method-optpp_cg
   method-optpp_q_newton
   method-optpp_fd_newton
   method-optpp_g_newton
   method-optpp_newton
   method-optpp_pds
   method-demo_tpl
   method-rol
   method-asynch_pattern_search
   method-mesh_adaptive_search
   method-nowpac
   method-snowpac
   method-moga
   method-soga
   method-coliny_pattern_search
   method-coliny_solis_wets
   method-coliny_cobyla
   method-coliny_direct
   method-coliny_ea
   method-coliny_beta
   method-nl2sol
   method-nonlinear_cg
   method-ncsu_direct
   method-genie_opt_darts
   method-genie_direct
   method-efficient_global
   method-surrogate_based_uq
   method-function_train
   method-multifidelity_function_train
   method-multilevel_function_train
   method-polynomial_chaos
   method-multifidelity_polynomial_chaos
   method-multilevel_polynomial_chaos
   method-stoch_collocation
   method-multifidelity_stoch_collocation
   method-sampling
   method-multilevel_sampling
   method-multifidelity_sampling
   method-multilevel_multifidelity_sampling
   method-approximate_control_variate
   method-importance_sampling
   method-gpais
   method-adaptive_sampling
   method-pof_darts
   method-rkd_darts
   method-global_evidence
   method-global_interval_est
   method-bayes_calibration
   method-dace
   method-fsu_cvt
   method-psuade_moat
   method-local_evidence
   method-local_interval_est
   method-local_reliability
   method-global_reliability
   method-fsu_quasi_mc
   method-vector_parameter_study
   method-list_parameter_study
   method-centered_parameter_study
   method-multidim_parameter_study
   method-richardson_extrap


**Specification**

- *Alias:* None

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+---------------------------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword                        | Dakota Keyword Description                    |
|                         | Group              |                                       |                                               |
+=========================+====================+=======================================+===============================================+
| Optional                                     | `id_method`__                         | Name the method block; helpful when there are |
|                                              |                                       | multiple                                      |
+----------------------------------------------+---------------------------------------+-----------------------------------------------+
| Optional                                     | `output`__                            | Control how much method information is        |
|                                              |                                       | written to the screen and output file         |
+----------------------------------------------+---------------------------------------+-----------------------------------------------+
| Optional                                     | `final_solutions`__                   | Number of designs returned as the best        |
|                                              |                                       | solutions                                     |
+-------------------------+--------------------+---------------------------------------+-----------------------------------------------+
| Required (Choose One)   | Method (Iterative  | `hybrid`__                            | Strategy in which a set of methods            |
|                         | Algorithm)         |                                       | synergistically seek an optimal design        |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `multi_start`__                       | Multi-Start Optimization Method               |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `pareto_set`__                        | Pareto set optimization                       |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `branch_and_bound`__                  | (Experimental Capability) Solves a mixed      |
|                         |                    |                                       | integer nonlinear optimization problem        |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `surrogate_based_local`__             | Local Surrogate Based Optimization            |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `surrogate_based_global`__            | Adaptive Global Surrogate-Based Optimization  |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `dot_frcg`__                          | DOT conjugate gradient optimization method    |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `dot_mmfd`__                          | DOT modified method of feasible directions    |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `dot_bfgs`__                          | DOT BFGS optimization method                  |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `dot_slp`__                           | DOT Sequential Linear Program                 |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `dot_sqp`__                           | DOT Sequential Quadratic Program              |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `conmin_frcg`__                       | CONMIN conjugate gradient optimization method |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `conmin_mfd`__                        | CONMIN method of feasible directions          |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `dl_solver`__                         | (Experimental) Dynamically-loaded solver      |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `npsol_sqp`__                         | NPSOL Sequential Quadratic Program            |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `nlssol_sqp`__                        | Sequential Quadratic Program for nonlinear    |
|                         |                    |                                       | least squares                                 |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `nlpql_sqp`__                         | NLPQL Sequential Quadratic Program            |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `optpp_cg`__                          | A conjugate gradient optimization method      |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `optpp_q_newton`__                    | Quasi-Newton optimization method              |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `optpp_fd_newton`__                   | Finite Difference Newton optimization method  |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `optpp_g_newton`__                    | Newton method based least-squares calbration  |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `optpp_newton`__                      | Newton method based optimization              |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `optpp_pds`__                         | Simplex-based derivative free optimization    |
|                         |                    |                                       | method                                        |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `demo_tpl`__                          | Third-party optimization library integration  |
|                         |                    |                                       | demonstration.                                |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `rol`__                               | Rapid Optimization Library (ROL) is a         |
|                         |                    |                                       | large-scale optimization package within       |
|                         |                    |                                       | Trilinos.                                     |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `asynch_pattern_search`__             | Pattern search, derivative free optimization  |
|                         |                    |                                       | method                                        |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `mesh_adaptive_search`__              | Finds optimal variable values using adaptive  |
|                         |                    |                                       | mesh-based search                             |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `nowpac`__                            | Gradient-free inequality-constrained          |
|                         |                    |                                       | optimization using Nonlinear Optimization     |
|                         |                    |                                       | With Path Augmented Constraints (NOWPAC).     |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `snowpac`__                           | Stochastic version of NOWPAC that             |
|                         |                    |                                       | incorporates error estimates and noise        |
|                         |                    |                                       | mitigation.                                   |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `moga`__                              | Multi-objective Genetic Algorithm (a.k.a      |
|                         |                    |                                       | Evolutionary Algorithm)                       |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `soga`__                              | Single-objective Genetic Algorithm (a.k.a     |
|                         |                    |                                       | Evolutionary Algorithm)                       |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `coliny_pattern_search`__             | Pattern search, derivative free optimization  |
|                         |                    |                                       | method                                        |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `coliny_solis_wets`__                 | Simple greedy local search method             |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `coliny_cobyla`__                     | Constrained Optimization BY Linear            |
|                         |                    |                                       | Approximations (COBYLA)                       |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `coliny_direct`__                     | DIviding RECTangles method                    |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `coliny_ea`__                         | Evolutionary Algorithm                        |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `coliny_beta`__                       | (Experimental) Coliny beta solver             |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `nl2sol`__                            | Trust-region method for nonlinear least       |
|                         |                    |                                       | squares                                       |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `nonlinear_cg`__                      | (Experimental) nonlinear conjugate gradient   |
|                         |                    |                                       | optimization                                  |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `ncsu_direct`__                       | DIviding RECTangles method                    |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `genie_opt_darts`__                   | Voronoi-based high-dimensional global         |
|                         |                    |                                       | Lipschitzian optimization                     |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `genie_direct`__                      | Classical high-dimensional global             |
|                         |                    |                                       | Lipschitzian optimization Classical           |
|                         |                    |                                       | high-dimensional global Lipschitzian          |
|                         |                    |                                       | optimization                                  |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `efficient_global`__                  | Global Surrogate Based Optimization, a.k.a.   |
|                         |                    |                                       | EGO                                           |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `surrogate_based_uq`__                | Generic UQ method for constructing and        |
|                         |                    |                                       | interrogating a surrogate model.              |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `function_train`__                    | UQ method leveraging a functional tensor      |
|                         |                    |                                       | train surrogate model.                        |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `multifidelity_function_train`__      | Multifidelity uncertainty quantification      |
|                         |                    |                                       | using function train expansions               |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `multilevel_function_train`__         | Multilevel uncertainty quantification using   |
|                         |                    |                                       | function train expansions                     |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `polynomial_chaos`__                  | Uncertainty quantification using polynomial   |
|                         |                    |                                       | chaos expansions                              |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `multifidelity_polynomial_chaos`__    | Multifidelity uncertainty quantification      |
|                         |                    |                                       | using polynomial chaos expansions             |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `multilevel_polynomial_chaos`__       | Multilevel uncertainty quantification using   |
|                         |                    |                                       | polynomial chaos expansions                   |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `stoch_collocation`__                 | Uncertainty quantification with stochastic    |
|                         |                    |                                       | collocation                                   |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `multifidelity_stoch_collocation`__   | Multifidelity uncertainty quantification      |
|                         |                    |                                       | using stochastic collocation                  |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `sampling`__                          | Randomly samples variables according to their |
|                         |                    |                                       | distributions                                 |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `multilevel_sampling`__               | Multilevel sampling methods for UQ            |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `multifidelity_sampling`__            | Multifidelity sampling methods for UQ         |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `multilevel_multifidelity_sampling`__ | Multilevel-Multifidelity sampling methods for |
|                         |                    |                                       | UQ                                            |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `approximate_control_variate`__       | Approximate control variate (ACV) sampling    |
|                         |                    |                                       | methods for UQ                                |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `importance_sampling`__               | Importance sampling                           |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `gpais`__                             | Gaussian Process Adaptive Importance Sampling |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `adaptive_sampling`__                 | (Experimental) Adaptively refine a Gaussian   |
|                         |                    |                                       | process surrogate                             |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `pof_darts`__                         | Probability-of-Failure (POF) darts is a novel |
|                         |                    |                                       | method for estimating the probability of      |
|                         |                    |                                       | failure based on random sphere-packing.       |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `rkd_darts`__                         | Recursive k-d (RKD) Darts: Recursive          |
|                         |                    |                                       | Hyperplane Sampling for Numerical Integration |
|                         |                    |                                       | of High-Dimensional Functions.                |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `global_evidence`__                   | Evidence theory with evidence measures        |
|                         |                    |                                       | computed with global optimization methods     |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `global_interval_est`__               | Interval analysis using global optimization   |
|                         |                    |                                       | methods                                       |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `bayes_calibration`__                 | Bayesian calibration                          |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `dace`__                              | Design and Analysis of Computer Experiments   |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `fsu_cvt`__                           | Design of Computer Experiments - Centroidal   |
|                         |                    |                                       | Voronoi Tessellation                          |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `psuade_moat`__                       | Morris One-at-a-Time                          |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `local_evidence`__                    | Evidence theory with evidence measures        |
|                         |                    |                                       | computed with local optimization methods      |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `local_interval_est`__                | Interval analysis using local optimization    |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `local_reliability`__                 | Local reliability method                      |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `global_reliability`__                | Global reliability methods                    |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `fsu_quasi_mc`__                      | Design of Computer Experiments - Quasi-Monte  |
|                         |                    |                                       | Carlo sampling                                |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `vector_parameter_study`__            | Samples variables along a user-defined vector |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `list_parameter_study`__              | Samples variables as a specified values       |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `centered_parameter_study`__          | Samples variables along points moving out     |
|                         |                    |                                       | from a center point                           |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `multidim_parameter_study`__          | Samples variables on full factorial grid of   |
|                         |                    |                                       | study points                                  |
|                         |                    +---------------------------------------+-----------------------------------------------+
|                         |                    | `richardson_extrap`__                 | Estimate order of convergence of a response   |
|                         |                    |                                       | as model fidelity increases                   |
+-------------------------+--------------------+---------------------------------------+-----------------------------------------------+

.. __: method-id_method.html
__ method-output.html
__ method-final_solutions.html
__ method-hybrid.html
__ method-multi_start.html
__ method-pareto_set.html
__ method-branch_and_bound.html
__ method-surrogate_based_local.html
__ method-surrogate_based_global.html
__ method-dot_frcg.html
__ method-dot_mmfd.html
__ method-dot_bfgs.html
__ method-dot_slp.html
__ method-dot_sqp.html
__ method-conmin_frcg.html
__ method-conmin_mfd.html
__ method-dl_solver.html
__ method-npsol_sqp.html
__ method-nlssol_sqp.html
__ method-nlpql_sqp.html
__ method-optpp_cg.html
__ method-optpp_q_newton.html
__ method-optpp_fd_newton.html
__ method-optpp_g_newton.html
__ method-optpp_newton.html
__ method-optpp_pds.html
__ method-demo_tpl.html
__ method-rol.html
__ method-asynch_pattern_search.html
__ method-mesh_adaptive_search.html
__ method-nowpac.html
__ method-snowpac.html
__ method-moga.html
__ method-soga.html
__ method-coliny_pattern_search.html
__ method-coliny_solis_wets.html
__ method-coliny_cobyla.html
__ method-coliny_direct.html
__ method-coliny_ea.html
__ method-coliny_beta.html
__ method-nl2sol.html
__ method-nonlinear_cg.html
__ method-ncsu_direct.html
__ method-genie_opt_darts.html
__ method-genie_direct.html
__ method-efficient_global.html
__ method-surrogate_based_uq.html
__ method-function_train.html
__ method-multifidelity_function_train.html
__ method-multilevel_function_train.html
__ method-polynomial_chaos.html
__ method-multifidelity_polynomial_chaos.html
__ method-multilevel_polynomial_chaos.html
__ method-stoch_collocation.html
__ method-multifidelity_stoch_collocation.html
__ method-sampling.html
__ method-multilevel_sampling.html
__ method-multifidelity_sampling.html
__ method-multilevel_multifidelity_sampling.html
__ method-approximate_control_variate.html
__ method-importance_sampling.html
__ method-gpais.html
__ method-adaptive_sampling.html
__ method-pof_darts.html
__ method-rkd_darts.html
__ method-global_evidence.html
__ method-global_interval_est.html
__ method-bayes_calibration.html
__ method-dace.html
__ method-fsu_cvt.html
__ method-psuade_moat.html
__ method-local_evidence.html
__ method-local_interval_est.html
__ method-local_reliability.html
__ method-global_reliability.html
__ method-fsu_quasi_mc.html
__ method-vector_parameter_study.html
__ method-list_parameter_study.html
__ method-centered_parameter_study.html
__ method-multidim_parameter_study.html
__ method-richardson_extrap.html



**Description**


The ``method`` keyword signifies the start of a block in the Dakota
input file.  A method block contains the various keywords necessary to
select a method and to control its behavior.

*Method Block Requirements*

At least one ``method`` block must appear in the Dakota input
file.  Multiple ``method`` blocks may be needed to fully define
advanced analysis approaches.

Each ``method`` block must specify one method and, optionally, any
associated keywords that govern the behavior of the method.

*The Methods*

Each ``method`` block must select one method.

Starting with Dakota v6.0, the methods are grouped into two types:
standard methods and multi-component methods.

The standard methods are
stand-alone and self-contained in the sense that they only require
a model to perform a study. They do not call other methods.
While methods such as
``polynomial_chaos`` and ``efficient_global`` internally utilize multiple
iterator and surrogate model components, these components are
generally hidden from user control due to restrictions on modularity;
thus, these methods are stand-alone.

The multi-component group
of methods provides a higher level "meta-algorithm" that points to
other methods and models that support sub-iteration.
For example, in a sequential hybrid method, the ``hybrid``
method specification must identify a list of subordinate methods, and
the "meta-algorithm" executes these methods in sequence and transfers
information between them. Surrogate-based minimizers provide another
example in that they point both to other methods (e.g. what
optimization method is used to solve the approximate subproblem) as
well as to models (e.g. what type of surrogate model is employed).
Multi-component methods generally provide some level of "plug and
play" modularity, through their flexible support of a variety of
method and model selections.

*Component-Based Iterator Commands*

Component-based iterator specifications include hybrid, multi-start,
pareto set, surrogate-based local, surrogate-based global, and branch
and bound methods. Whereas a standard iterator specification only
needs an optional model pointer string (specified with
``model_pointer``), component-based iterator specifications can include
method pointer, method name, and model pointer specifications in order
to define the components employed in the "meta-iteration." In
particular, these specifications identify one or more methods (by
pointer or by name) to specify the subordinate iterators that will be
used in the top-level algorithm. Identifying a sub-iterator by name
instead of by pointer is a lightweight option that relaxes the need
for a separate method specification for the sub-iterator; however, a
model pointer may be required in this case to provide the
specification connectivity normally supported by the method pointer.
Refer to these individual method descriptions for specific
requirements for these advanced methods.




*Method Independent Controls*

In addition to the method, there are 10 optional keywords, which
are referred to as method independent controls.
These controls are valid for enough methods that it was
reasonable to pull them out of the method dependent blocks and consolidate the
specifications, however, they are NOT universally respected by all methods.



**Examples**


Several examples follow. The first example shows a minimal
specification for an optimization method.

.. code-block::

    method
      dot_sqp

This example uses all of the defaults for this method.

A more sophisticated example would be

.. code-block::

    method,
      id_method = 'NLP1'
      dot_sqp
        max_iterations = 50
        convergence_tolerance = 1e-4
        output verbose
        model_pointer = 'M1'

This example demonstrates the use of identifiers and pointers
as well as some method independent and method
dependent controls for the sequential quadratic programming (SQP)
algorithm from the DOT library. The ``max_iterations``,
``convergence_tolerance``, and ``output`` settings are method independent
controls, in that they are defined for a variety of methods.

The next example shows a specification for a least squares method.

.. code-block::

    method
      optpp_g_newton
        max_iterations = 10
        convergence_tolerance = 1.e-8
        search_method trust_region
        gradient_tolerance = 1.e-6

Some of the same method independent controls are present along with
several method dependent controls ( ``search_method`` and
``gradient_tolerance``) which are only meaningful for OPT++ methods (see
:ref:`topic-package_optpp`).

The next example shows a specification for a nondeterministic method
with several method dependent controls (refer to :dakkw:`method-sampling`).

.. code-block::

    method
      sampling
        samples = 100
        seed = 12345
        sample_type lhs
        response_levels = 1000. 500.


The last example shows a specification for a parameter study method
where, again, each of the controls are method dependent (refer to
:dakkw:`method-vector_parameter_study`).

.. code-block::

    method
      vector_parameter_study
        step_vector = 1. 1. 1.
        num_steps = 10




