Blurb::
Local Surrogate Based Optimization
Description::
In surrogate-based optimization (SBO) and surrogate-based nonlinear
least squares (SBNLS), minimization occurs using a set of one or more
approximations, defined from a surrogate model, that are built and
periodically updated using data from a "truth" model. The surrogate
model can be a global data fit (e.g., regression or interpolation of
data generated from a design of computer experiments), a multipoint
approximation, a local Taylor Series expansion, or a model hierarchy
approximation (e.g., a low-fidelity simulation model), whereas the
truth model involves a high-fidelity simulation model. The goals of
surrogate-based methods are to reduce the total number of truth model
simulations and, in the case of global data fit surrogates, to smooth
noisy data with an easily navigated analytic function.

In the surrogate-based local method, a trust region approach is used
to manage the minimization process to maintain acceptable accuracy
between the surrogate model and the truth model (by limiting the range
over which the surrogate model is trusted). The process involves a
sequence of minimizations performed on the surrogate model and bounded
by the trust region. At the end of each approximate minimization, the
candidate optimum point is validated using the truth model. If
sufficient decrease has been obtained in the truth model, the trust
region is re-centered around the candidate optimum point and the trust
region will either shrink, expand, or remain the same size depending
on the accuracy with which the surrogate model predicted the truth
model decrease. If sufficient decrease has not been attained, the
trust region center is not updated and the entire trust region shrinks
by a user-specified factor. The cycle then repeats with the
construction of a new surrogate model, a minimization, and another
test for sufficient decrease in the truth model. This cycle continues
until convergence is attained.

*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)
Topics::
surrogate_based_optimization_methods
Examples::

Theory::
For surrogate_based_local problems with nonlinear constraints, a
number of algorithm formulations exist as described in :cite:p:`Eld06b`
and as summarized in :ref:`adv_meth:sbm:sblm`.
Faq::

See_Also::
