# PyUNLocBoX: convex optimization in Python¶

The PyUNLocBoX is a convex optimization package based on proximal splitting methods and implemented in Python (a Matlab counterpart exists). It is a free software, distributed under the BSD license, and available on PyPI. The documentation is available online and development takes place on GitHub.

The package is designed to be easy to use while allowing any advanced tasks. It is not meant to be a black-box optimization tool. You’ll have to carefully design your solver. In exchange you’ll get full control of what the package does for you, without the pain of rewriting the proximity operators and the solvers and with the added benefit of tested algorithms. With this package, you can focus on your problem and the best way to solve it rather that the details of the algorithms. It comes with the following solvers:

• Forward-backward splitting algorithm (FISTA, ISTA)
• Douglas-Rachford splitting algorithm
• Generalized forward-backward
• Monotone+Lipschitz forward-backward-forward primal-dual algorithm
• Projection-based primal-dual algorithm

Moreover, the following acceleration schemes are included:

• FISTA acceleration scheme
• Backtracking based on a quadratic approximation of the objective
• Regularized nonlinear acceleration (RNA)

To compose your objective, you can either define your custom functions (which should implement an evaluation method and a gradient or proximity method) or use one of the followings:

• L1-norm
• L2-norm
• TV-norm
• Nuclear-norm
• Projection on the L2-ball

Following is a typical usage example who solves an optimization problem composed by the sum of two convex functions. The functions and solver objects are first instantiated with the desired parameters. The problem is then solved by a call to the solving function.

>>> import pyunlocbox
>>> f1 = pyunlocbox.functions.norm_l2(y=[4, 5, 6, 7])
>>> f2 = pyunlocbox.functions.dummy()
>>> solver = pyunlocbox.solvers.forward_backward()
>>> ret = pyunlocbox.solvers.solve([f1, f2], [0., 0, 0, 0], solver, atol=1e-5)
Solution found after 9 iterations:
objective function f(sol) = 6.714385e-08
stopping criterion: ATOL
>>> ret['sol']
array([ 3.99990766,  4.99988458,  5.99986149,  6.99983841])


## Installation¶

The PyUnLocBox is available on PyPI:

$pip install pyunlocbox  ## Contributing¶ The development of this package takes place on GitHub. Issues and pull requests are welcome. You can improve or add solvers, functions, and acceleration schemes in pyunlocbox/solvers.py, pyunlocbox/functions.py, and pyunlocbox/acceleration.py, along with their corresponding unit tests in pyunlocbox/tests/test_*.py (with reasonable coverage) and documentation in doc/reference/*.rst. If you have a nice example to demonstrate the use of the introduced functionality, please consider adding a tutorial in doc/tutorials. Do not forget to update README.rst and doc/history.rst with e.g. new features or contributors. The version number needs to be updated in setup.py and pyunlocbox/__init__.py. Please make sure that your changes pass the tests (enforced by CI) and check the generated coverage report at htmlcov/index.html to make sure the tests reasonably cover the changes you’ve introduced: $ make lint
$make test$ make docall


## Authors¶

PyUNLocBoX was started in 2014 as an academic project for research purpose at the EPFL LTS2 laboratory.