Blurb::
Select a search method for Newton-based optimizers
Description::
The ``search_method`` control is defined for all Newton-based
optimizers and is used to select between ``trust_region``,
``gradient_based_line_search``, and ``value_based_line_search`` methods.
The ``gradient_based_line_search`` option uses the line search method
proposed by :cite:p:`More1994`. This option
satisfies sufficient decrease and curvature conditions; whereas,
``value_base_line_search`` only satisfies the sufficient decrease
condition. At each line search iteration, the
``gradient_based_line_search`` method computes the function and gradient
at the trial point. Consequently, given expensive function
evaluations, the ``value_based_line_search`` method is preferred to the
``gradient_based_line_search`` method. Each of these Newton methods
additionally supports the ``tr_pds`` selection for unconstrained
problems. This option performs a robust trust region search using
pattern search techniques. Use of a line search is the default for
bound-constrained and generally-constrained problems, and use of a
``trust_region`` search method is the default for unconstrained problems.
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