| Name | trustregion JSON |
| Version |
1.2.1
JSON |
| download |
| home_page | None |
| Summary | Trust-region subproblem solvers for nonlinear/nonconvex optimization |
| upload_time | 2024-05-31 02:16:57 |
| maintainer | None |
| docs_url | None |
| author | None |
| requires_python | >=3.8 |
| license | GPL-3.0-or-later |
| keywords |
mathematics
optimization
|
| VCS |
 |
| bugtrack_url |
|
| requirements |
No requirements were recorded.
|
| Travis-CI |
No Travis.
|
| coveralls test coverage |
No coveralls.
|
===========================================
trustregion: Trust-region subproblem solver
===========================================
.. image:: https://github.com/lindonroberts/trust-region/actions/workflows/python_testing.yml/badge.svg
:target: https://github.com/lindonroberts/trust-region/actions
:alt: Build Status
.. image:: https://img.shields.io/badge/License-GPL%20v3-blue.svg
:target: https://www.gnu.org/licenses/gpl-3.0
:alt: GNU GPL v3 License
.. image:: https://img.shields.io/pypi/v/trustregion.svg
:target: https://pypi.python.org/pypi/trustregion
:alt: Latest PyPI version
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
.. code-block::
min_{s in R^n} g^T s + 0.5 s^T H s, subject to ||s||_2 <= delta (and sl <= s <= su)
**Quick install**
.. code-block:: bash
$ sudo apt-get install gfortran
$ pip install --user numpy
$ pip install --user trustregion
For more details, see below. Note that NumPy must be installed first, as it is used to compile the Fortran-linked modules.
**Interface**
The Python package :code:`trustregion` provides one routine, :code:`solve`, with interface:
.. code-block:: python
import trustregion
s = trustregion.solve(g, H, delta, sl=None, su=None, verbose_output=False)
s, gnew, crvmin = trustregion.solve(g, H, delta, sl=None, su=None, verbose_output=True)
where the inputs are
* :code:`g`, the gradient of the objective (as a 1D NumPy array)
* :code:`H`, the symmetric Hessian matrix of the objective (as a 2D square NumPy array) - this can be :code:`None` if the model is linear
* :code:`delta`, the trust-region radius (non-negative float)
* :code:`sl`, the lower bounds on the step (as a 1D NumPy array) - this can be :code:`None` if not present, but :code:`sl` and :code:`su` must either be both :code:`None` or both set
* :code:`su`, the upper bounds on the step (as a 1D NumPy array) - this can be :code:`None` if not present, but :code:`sl` and :code:`su` must either be both :code:`None` or both set
* :code:`verbose_output`, a flag indicating which outputs to return.
The outputs are:
* :code:`s`, an approximate minimizer of the subproblem (as a 1D NumPy array)
* :code:`gnew`, the gradient of the objective at the solution :code:`s` (i.e. :code:`gnew = g + H.dot(s)`)
* :code:`crvmin`, a float giving information about the curvature of the problem. If :code:`s` is on the trust-region boundary (given by :code:`delta`), then :code:`crvmin=0`. If :code:`s` is constrained in all directions by the box constraints, then :code:`crvmin=-1`. Otherwise, :code:`crvmin>0` is the smallest curvature seen in the Hessian.
**Example Usage**
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.
**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].
* :code:`trsbox.f90` solves the quadratic case with box constraints. It is a minor modification of the routine of the same name in :code:`BOBYQA` [M. J. D. Powell (2009), `The BOBYQA algorithm for bound constrained optimization without derivatives <http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf>`_, technical report DAMTP 2009/NA06, University of Cambridge].
In the linear case, an active-set method is used to solve the resulting convex problem. In the quadratic cases, a modification of the Steihaug-Toint/conjugate gradient method is used. For more details, see the relevant references above.
Requirements
------------
:code:`trustregion` requires the following software to be installed:
* Fortran compiler (e.g. gfortran)
* Python 3.8 or higher (http://www.python.org/)
Additionally, the following python packages should be installed (these will be installed automatically if using *pip*, see `Installation using pip`_):
* NumPy (http://www.numpy.org/)
Installation using pip
----------------------
For easy installation, use `pip <http://www.pip-installer.org/>`_ as root:
.. code-block:: bash
$ [sudo] pip install numpy
$ [sudo] pip install trustregion
Note that NumPy should be installed before :code:`trustregion`, as it is used to compile the Fortran modules.
If you do not have root privileges or you want to install :code:`trustregion` for your private use, you can use:
.. code-block:: bash
$ pip install --user numpy
$ pip install --user trustregion
which will install :code:`trustregion` in your home directory.
Note that if an older install of :code:`trustregion` is present on your system you can use:
.. code-block:: bash
$ [sudo] pip install --upgrade trustregion
to upgrade :code:`trustregion` to the latest version.
Manual installation
-------------------
Alternatively, you can download the source code from `Github <https://github.com/lindonroberts/trust-region>`_ and unpack as follows:
.. code-block:: bash
$ git clone https://github.com/lindonroberts/trust-region
$ cd trust-region
To upgrade :code:`trustregion` to the latest version, navigate to the top-level directory (i.e. the one containing :code:`setup.py`) and rerun the installation using :code:`pip`, as above:
.. code-block:: bash
$ git pull
$ [sudo] pip install . # with admin privileges
Testing
-------
If you installed :code:`trustregion` manually, you can test your installation by running:
.. code-block:: bash
$ pip install pytest
$ cd trustregion/tests
$ python -m pytest
Alternatively, the documentation provides some simple examples of how to run :code:`trustregion`.
Uninstallation
--------------
If :code:`trustregion` was installed using *pip* you can uninstall as follows:
.. code-block:: bash
$ [sudo] pip uninstall trustregion
If :code:`trustregion` was installed manually you have to remove the installed files by hand (located in your python site-packages directory).
Bugs
----
Please report any bugs using GitHub's issue tracker.
License
-------
This algorithm is released under the GNU GPL license.
Raw data
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"description": "===========================================\ntrustregion: Trust-region subproblem solver\n===========================================\n\n.. image:: https://github.com/lindonroberts/trust-region/actions/workflows/python_testing.yml/badge.svg\n :target: https://github.com/lindonroberts/trust-region/actions\n :alt: Build Status\n\n.. image:: https://img.shields.io/badge/License-GPL%20v3-blue.svg\n :target: https://www.gnu.org/licenses/gpl-3.0\n :alt: GNU GPL v3 License\n\n.. image:: https://img.shields.io/pypi/v/trustregion.svg\n :target: https://pypi.python.org/pypi/trustregion\n :alt: Latest PyPI version\n\nThis 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.\n\nThe trust-region subproblem we solve is\n\n.. code-block::\n\n min_{s in R^n} g^T s + 0.5 s^T H s, subject to ||s||_2 <= delta (and sl <= s <= su)\n\n**Quick install**\n\n .. code-block:: bash\n\n $ sudo apt-get install gfortran\n $ pip install --user numpy\n $ pip install --user trustregion\n\nFor more details, see below. Note that NumPy must be installed first, as it is used to compile the Fortran-linked modules.\n\n**Interface** \n\nThe Python package :code:`trustregion` provides one routine, :code:`solve`, with interface:\n\n .. code-block:: python\n\n import trustregion\n s = trustregion.solve(g, H, delta, sl=None, su=None, verbose_output=False)\n s, gnew, crvmin = trustregion.solve(g, H, delta, sl=None, su=None, verbose_output=True)\n\nwhere the inputs are\n\n* :code:`g`, the gradient of the objective (as a 1D NumPy array)\n* :code:`H`, the symmetric Hessian matrix of the objective (as a 2D square NumPy array) - this can be :code:`None` if the model is linear\n* :code:`delta`, the trust-region radius (non-negative float)\n* :code:`sl`, the lower bounds on the step (as a 1D NumPy array) - this can be :code:`None` if not present, but :code:`sl` and :code:`su` must either be both :code:`None` or both set\n* :code:`su`, the upper bounds on the step (as a 1D NumPy array) - this can be :code:`None` if not present, but :code:`sl` and :code:`su` must either be both :code:`None` or both set\n* :code:`verbose_output`, a flag indicating which outputs to return.\n\nThe outputs are:\n\n* :code:`s`, an approximate minimizer of the subproblem (as a 1D NumPy array)\n* :code:`gnew`, the gradient of the objective at the solution :code:`s` (i.e. :code:`gnew = g + H.dot(s)`)\n* :code:`crvmin`, a float giving information about the curvature of the problem. If :code:`s` is on the trust-region boundary (given by :code:`delta`), then :code:`crvmin=0`. If :code:`s` is constrained in all directions by the box constraints, then :code:`crvmin=-1`. Otherwise, :code:`crvmin>0` is the smallest curvature seen in the Hessian.\n\n**Example Usage** \n\nExamples 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.\n\n**Algorithms**\n\n:code:`trustregion` implements three different methods for solving the subproblem, based on the problem class (in Fortran 90, wrapped to Python):\n\n* :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.\n* :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].\n* :code:`trsbox.f90` solves the quadratic case with box constraints. It is a minor modification of the routine of the same name in :code:`BOBYQA` [M. J. D. Powell (2009), `The BOBYQA algorithm for bound constrained optimization without derivatives <http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2009_06.pdf>`_, technical report DAMTP 2009/NA06, University of Cambridge].\n\nIn the linear case, an active-set method is used to solve the resulting convex problem. In the quadratic cases, a modification of the Steihaug-Toint/conjugate gradient method is used. For more details, see the relevant references above.\n\nRequirements\n------------\n:code:`trustregion` requires the following software to be installed:\n\n* Fortran compiler (e.g. gfortran)\n* Python 3.8 or higher (http://www.python.org/)\n\nAdditionally, the following python packages should be installed (these will be installed automatically if using *pip*, see `Installation using pip`_):\n\n* NumPy (http://www.numpy.org/)\n\nInstallation using pip\n----------------------\nFor easy installation, use `pip <http://www.pip-installer.org/>`_ as root:\n\n .. code-block:: bash\n\n $ [sudo] pip install numpy\n $ [sudo] pip install trustregion\n\nNote that NumPy should be installed before :code:`trustregion`, as it is used to compile the Fortran modules.\n\nIf you do not have root privileges or you want to install :code:`trustregion` for your private use, you can use:\n\n .. code-block:: bash\n\n $ pip install --user numpy\n $ pip install --user trustregion\n\nwhich will install :code:`trustregion` in your home directory.\n\nNote that if an older install of :code:`trustregion` is present on your system you can use:\n\n .. code-block:: bash\n\n $ [sudo] pip install --upgrade trustregion\n\nto upgrade :code:`trustregion` to the latest version.\n\nManual installation\n-------------------\nAlternatively, you can download the source code from `Github <https://github.com/lindonroberts/trust-region>`_ and unpack as follows:\n\n .. code-block:: bash\n\n $ git clone https://github.com/lindonroberts/trust-region\n $ cd trust-region\n\nTo upgrade :code:`trustregion` to the latest version, navigate to the top-level directory (i.e. the one containing :code:`setup.py`) and rerun the installation using :code:`pip`, as above:\n\n .. code-block:: bash\n\n $ git pull\n $ [sudo] pip install . # with admin privileges\n\nTesting\n-------\nIf you installed :code:`trustregion` manually, you can test your installation by running:\n\n .. code-block:: bash\n\n $ pip install pytest\n $ cd trustregion/tests\n $ python -m pytest\n\nAlternatively, the documentation provides some simple examples of how to run :code:`trustregion`.\n\nUninstallation\n--------------\nIf :code:`trustregion` was installed using *pip* you can uninstall as follows:\n\n .. code-block:: bash\n\n $ [sudo] pip uninstall trustregion\n\nIf :code:`trustregion` was installed manually you have to remove the installed files by hand (located in your python site-packages directory).\n\nBugs\n----\nPlease report any bugs using GitHub's issue tracker.\n\nLicense\n-------\nThis algorithm is released under the GNU GPL license.\n",
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