Blurb::
NPSOL Sequential Quadratic Program
Description::
Sequential quadratic programming optimizer.

*NPSOL requires a separate software license and therefore may not
be available in all versions of Dakota.  CONMIN or OPT++ methods may
be suitable alternatives.*


*Stopping Criteria*

The method independent controls for ``max_iterations`` and
``max_function_evaluations`` limit the number of major SQP iterations and
the number of function evaluations that can be performed during an
NPSOL optimization. The ``convergence_tolerance`` control defines
NPSOL's internal optimality tolerance which is used in evaluating if
an iterate satisfies the first-order Kuhn-Tucker conditions for a
minimum. The magnitude of ``convergence_tolerance`` approximately
specifies the number of significant digits of accuracy desired in the
final objective function (e.g., ``convergence_tolerance`` = ``1``.e-6
will result in approximately six digits of accuracy in the final
objective function). The ``constraint_tolerance`` control defines how
tightly the constraint functions are satisfied at convergence. The
default value is dependent upon the machine precision of the platform
in use, but is typically on the order of ``1``.e-8 for double precision
computations. Extremely small values for ``constraint_tolerance`` may
not be attainable. The ``output`` verbosity setting controls the amount
of information generated at each major SQP iteration: the ``silent``
and ``quiet`` settings result in only one line of diagnostic output for
each major iteration and print the final optimization solution,
whereas the ``verbose`` and ``debug`` settings add additional
information on the objective function, constraints, and variables at
each major iteration.


*Concurrency*

NPSOL is not a parallel algorithm and cannot directly take advantage
of concurrent evaluations. However, if ``numerical_gradients`` with
``method_source`` ``dakota`` is specified, then the finite difference
function evaluations can be performed concurrently (using any of
:ref:`the parallel modes <parallel>`).

An important related
observation is the fact that NPSOL uses two different line searches
depending on how gradients are computed. For either
``analytic_gradients`` or ``numerical_gradients`` with ``method_source``
``dakota``, NPSOL is placed in user-supplied gradient mode (NPSOL's
"Derivative Level" is set to 3) and it uses a gradient-based line
search (the assumption is that user-supplied gradients are
inexpensive). On the other hand, if ``numerical_gradients`` are
selected with ``method_source`` ``vendor``, then NPSOL is computing
finite differences internally and it will use a value-based line
search (the assumption is that finite differencing on each line search
evaluation is too expensive). The ramifications of this are: (1)
performance will vary between ``method_source`` ``dakota`` and
``method_source`` ``vendor`` for ``numerical_gradients``, and (2) gradient
speculation is unnecessary when performing optimization in parallel
since the gradient-based line search in user-supplied gradient mode is
already load balanced for parallel execution. Therefore, a
``speculative`` specification will be ignored by NPSOL, and optimization
with numerical gradients should select ``method_source`` ``dakota`` for
load balanced parallel operation and ``method_source`` ``vendor`` for
efficient serial operation.


*Linear constraints*

Lastly, NPSOL supports specialized handling of linear inequality and
equality constraints. By specifying the coefficients and bounds of the
linear inequality constraints and the coefficients and targets of the
linear equality constraints, this information can be provided to NPSOL
at initialization and tracked internally, removing the need for the
user to provide the values of the linear constraints on every function
evaluation.

*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::
package_npsol, sequential_quadratic_programming, local_optimization_methods
Examples::

Theory::

Faq::

See_Also::
