Blurb::
Initial step size for derivative-free optimizers

Description::
The \c initial_delta keyword defines the size of the first search step
in derivative-free optimization methods, specifically \c
asynch_pattern_search, \c coliny_cobyla, \c coliny_pattern_search, \c
coliny_solis_wets, and \c mesh_adaptive_search.  It is applied in an
absolute sense to all search directions.

<b> Default Behavior </b>

The default value is 1.0.

<b> Usage Tips </b>

It is recommended that \c initial_delta be the approximate distance
from the initial point to the solution.  If this distance is unknown,
it is advisable to err on the side of choosing an \c initial_delta
that is too large or to not specify it.  Relative application of \c
initial_delta is not available unless the user scales the problem
accordingly.

Topics::

Examples::

Three example method input blocks appear below.

For \c asynch_pattern_search:
\verbatim
method
  asynch_pattern_search
    initial_delta = .5
    contraction_factor = 0.25
    merit_function merit1_smooth
    smoothing_factor = 1.0
    constraint_tolerance = 1.e-6
\endverbatim

For \c coliny_pattern_search:
\verbatim
method
  coliny_pattern_search
    initial_delta = .2
    variable_tolerance = 1.e-4
    max_iterations 100
    solution_accuracy = 1.e-6
    seed = 1234
    max_function_evaluations = 1000
\endverbatim

For \c mesh_adaptive_search
\verbatim
method
  mesh_adaptive_search
    initial_delta = 2.0
    seed = 1234
\endverbatim

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