Trust-region subproblem solvers for nonlinear/nonconvex optimization
Project description
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
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
$ 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 trustregion provides one routine, solve, with interface:
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
g, the gradient of the objective (as a 1D NumPy array)H, the symmetric Hessian matrix of the objective (as a 2D square NumPy array) - this can beNoneif the model is lineardelta, the trust-region radius (non-negative float)sl, the lower bounds on the step (as a 1D NumPy array) - this can beNoneif not present, butslandsumust either be bothNoneor both setsu, the upper bounds on the step (as a 1D NumPy array) - this can beNoneif not present, butslandsumust either be bothNoneor both setverbose_output, a flag indicating which outputs to return.
The outputs are:
s, an approximate minimizer of the subproblem (as a 1D NumPy array)gnew, the gradient of the objective at the solutions(i.e.gnew = g + H.dot(s))crvmin, a float giving information about the curvature of the problem. Ifsis on the trust-region boundary (given bydelta), thencrvmin=0. Ifsis constrained in all directions by the box constraints, thencrvmin=-1. Otherwise,crvmin>0is the smallest curvature seen in the Hessian.
Example Usage
Examples for the use of trustregion.solve can be found in the examples directory on Github.
Algorithms
trustregion implements three different methods for solving the subproblem, based on the problem class (in Fortran 90, wrapped to Python):
trslin.f90solves the linear objective case (whereH=NoneorH=0), using Algorithm B.1 from: L. Roberts (2019), Derivative-Free Algorithms for Nonlinear Optimisation Problems, PhD Thesis, University of Oxford.trsapp.f90solves the quadratic case without box constraints. It is a minor modification of the routine of the same name inNEWUOA[M. J. D. Powell (2004), The NEWUOA software for unconstrained optimization without derivatives, technical report DAMTP 2004/NA05, University of Cambridge].trsbox.f90solves the quadratic case with box constraints. It is a minor modification of the routine of the same name inBOBYQA[M. J. D. Powell (2009), The BOBYQA algorithm for bound constrained optimization without derivatives, 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
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:
$ pip install numpy $ pip install trustregion
Note that NumPy should be installed before trustregion, as it is used to compile the Fortran modules.
If you do not have root privileges or you want to install trustregion for your private use, you can use:
$ pip install --user numpy $ pip install --user trustregion
which will install trustregion in your home directory.
Alternatively, you can use pip inside a virtual environment using Python’s virtual environments or the conda environment manager.
Note that if an older install of trustregion is present on your system you can use:
$ pip install --upgrade trustregion
to upgrade trustregion to the latest version.
Manual installation
Alternatively, you can download the source code from Github and unpack as follows:
$ git clone https://github.com/lindonroberts/trust-region $ cd trust-region
To upgrade trustregion to the latest version, navigate to the top-level directory (i.e. the one containing setup.py) and rerun the installation using pip, as above:
$ git pull $ pip install .
Testing
If you installed trustregion manually, you can test your installation by running:
$ pip install pytest $ cd trustregion/tests $ python -m pytest
Alternatively, the documentation provides some simple examples of how to run trustregion.
Uninstallation
If trustregion was installed using pip you can uninstall as follows:
$ pip uninstall trustregion
If 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.
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