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lindonroberts authored Dec 4, 2019
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:target: https://www.gnu.org/licenses/gpl-3.0
:alt: GNU GPL v3 License

This package provides methods for solving the trust-region subproblem from nonlinear, nonconvex optimization. For more details on trust-region methods, see the book: A. R. Conn, N. I. M. Gould and Ph. L. Toint (2000), Trust-Region Methods, MPS-SIAM Series on Optimization.
This package provides Python routines for solving the trust-region subproblem from nonlinear, nonconvex optimization. For more details on trust-region methods, see the book: A. R. Conn, N. I. M. Gould and Ph. L. Toint (2000), Trust-Region Methods, MPS-SIAM Series on Optimization.

The trust-region subproblem we solve is

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**Interface**

The package :code:`trustregion` provides one routine, :code:`solve`, with interface:
The Python package :code:`trustregion` provides one routine, :code:`solve`, with interface:

.. code-block:: python
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Examples for the use of :code:`trustregion.solve` can be found in the `examples <https://github.com/lindonroberts/trust-region/tree/master/examples>`_ directory on Github.

Algorithm
---------
:code:`trustregion` implements three different methods for solving the subproblem, based on the problem class (in Fortran 90, wrapped to Python)
**Algorithms**

:code:`trustregion` implements three different methods for solving the subproblem, based on the problem class (in Fortran 90, wrapped to Python):

* :code:`trslin.f90` solves the linear objective case (where :code:`H=None` or :code:`H=0`), using Algorithm B.1 from: L. Roberts (2019), `Derivative-Free Algorithms for Nonlinear Optimisation Problems <https://ora.ox.ac.uk/objects/uuid:ec76e895-6eee-491a-88ed-b4ed10fa6003>`_, PhD Thesis, University of Oxford.
* :code:`trsapp.f90` solves the quadratic case without box constraints. It is a minor modification of the routine of the same name in :code:`NEWUOA` [M. J. D. Powell (2004), `The NEWUOA software for unconstrained optimization without derivatives <http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2004_08.pdf>`_, technical report DAMTP 2004/NA05, University of Cambridge].
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