PICOS

Introduction

PICOS is a user friendly Python API to several conic and integer programming solvers, designed to be used by both application developers and researchers as well as instructors teaching courses on mathematical optimization. It allows you to enter an optimization problem as a high level model, with painless support for (complex) vector and matrix variables and multidimensional algebra. Your model will be transformed to the standard form understood by an appropriate solver that is available at runtime. This makes your application portable as users have the choice between several commercial and open source solvers.

Features

PICOS supports the following solvers and problem types. To use a solver, you need to separately install it along with the Python interface listed here.

.. _Apache-2.0: https://www.apache.org/licenses/LICENSE-2.0 .. _GPL-3: https://www.gnu.org/licenses/gpl-3.0.html .. _MIT: https://opensource.org/licenses/MIT .. _ZIB: https://scip.zib.de/academic.txt

.. list-table:: :header-rows: 1

* - | Solver
    |
  - | Python
    | interface
  - | `LP <https://en.wikipedia.org/wiki/Linear_programming>`_
    |
  - | `SOCP <https://en.wikipedia.org/wiki/Second-order_cone_programming>`_,
    | `QCQP <https://en.wikipedia.org/wiki/Quadratically_constrained_quadratic_program>`_
  - | `SDP <https://en.wikipedia.org/wiki/Semidefinite_programming>`_
    |
  - | `EXP <https://docs.mosek.com/modeling-cookbook/expo.html>`_
    |
  - | `MIP <https://en.wikipedia.org/wiki/Integer_programming>`_
    |
  - | `QREP <https://en.wikipedia.org/wiki/Quantum_relative_entropy>`_
    |
  - | License
    |
* - `CPLEX <https://www.ibm.com/analytics/cplex-optimizer>`_
  - included
  - Yes
  - Yes
  -
  -
  - Yes
  -
  - non-free
* - `CVXOPT <https://cvxopt.org/>`_
  - native
  - Yes
  - Yes
  - Yes
  - `GP <https://en.wikipedia.org/wiki/Geometric_programming>`_
  -
  -
  - `GPL-3`_
* - `ECOS <https://github.com/embotech/ecos>`_
  - `ecos-python <https://github.com/embotech/ecos-python>`_
  - Yes
  - Yes
  -
  - Yes
  - Yes
  -
  - `GPL-3`_
* - `GLPK <https://www.gnu.org/software/glpk/>`_
  - `swiglpk <https://github.com/biosustain/swiglpk>`_
  - Yes
  -
  -
  -
  - Yes
  -
  - `GPL-3`_
* - `Gurobi <http://www.gurobi.com/products/gurobi-optimizer>`_
  - `gurobipy <https://www.gurobi.com>`_
  - Yes
  - Yes
  -
  -
  - Yes
  -
  - non-free
* - `MOSEK <https://www.mosek.com/>`_
  - included
  - Yes
  - Yes
  - Yes
  -
  - Yes
  -
  - non-free
* - `OSQP <https://osqp.org>`_
  - native
  - Yes
  - `QP <https://en.wikipedia.org/wiki/Quadratic_programming>`_
  -
  -
  -
  -
  - `Apache-2.0`_
* - `QICS <https://qics.readthedocs.io/en/stable/>`_
  - native
  - Yes
  - Yes
  - Yes
  - Yes
  -
  - Yes
  - `MIT`_
* - `SCIP <http://scip.zib.de/>`_
  - `PySCIPOpt <https://github.com/SCIP-Interfaces/PySCIPOpt/>`_
  - Yes
  - Yes
  -
  -
  - Yes
  -
  - `ZIB`_/`MIT`_
* - `SMCP <http://smcp.readthedocs.io/en/latest/>`_
  - native
  -
  -
  - Yes
  -
  -
  -
  - `GPL-3`_

.. rubric:: Example

This is what it looks like to solve a multidimensional mixed integer program with PICOS:

import picos as pc P = pc.Problem() x = pc.IntegerVariable("x", 2) P += 2*x <= 11 P.maximize = pc.sum(x) P.solve(solver="glpk") # Optional: Use GLPK as backend. <feasible primal solution (claimed optimal) from glpk> P.value 10.0 print(x) [ 5.00e+00] [ 5.00e+00]

You can head to our quick examples <https://picos-api.gitlab.io/picos/quick.html>_ or the tutorial <https://picos-api.gitlab.io/picos/tutorial.html>_ for more.

Installation

As of release 2.2, PICOS requires Python 3.4 or later.

.. rubric:: Via pip

If you are using pip <https://pypi.org/project/pip/>_ you can run pip install picos to get the latest version.

.. rubric:: Via Anaconda

If you are using Anaconda <https://anaconda.org/>_ you can run conda install -c picos picos to get the latest version.

.. rubric:: Via your system's package manager

.. list-table:: :header-rows: 1 :stub-columns: 1

* - Distribution
  - Latest major version
  - Latest version
* - Arch Linux
  - `python-picos <https://aur.archlinux.org/packages/python-picos/>`__
  - `python-picos-git <https://aur.archlinux.org/packages/python-picos-git/>`__

If you are packaging PICOS for additional platforms, please let us know.

.. rubric:: From source

The PICOS source code can be found on GitLab <https://gitlab.com/picos-api/picos>_. There are only two dependencies:

• NumPy <https://numpy.org/>_
• CVXOPT_

Documentation

The full documentation can be browsed online <https://picos-api.gitlab.io/picos/>__ or downloaded in PDF form <https://picos-api.gitlab.io/picos/picos.pdf>__.

Credits

.. rubric:: Developers

• Guillaume Sagnol <http://page.math.tu-berlin.de/~sagnol/>_ has started work on PICOS in 2012.
• Maximilian Stahlberg <https://orcid.org/0000-0002-0190-2693>_ is extending and co-maintaining PICOS since 2017.

.. rubric:: Contributors

For an up-to-date list of all code contributors, please refer to the contributors page <https://gitlab.com/picos-api/picos/-/graphs/master>. Should a reference from before 2019 be unclear, see also the old contributors page <https://github.com/gsagnol/picos/graphs/contributors> on GitHub.

Citing

The preferred way to cite PICOS in your research is our JOSS paper <https://joss.theoj.org/papers/10.21105/joss.03915>_:

.. code-block:: bibtex

@article{PICOS, author = {Guillaume Sagnol and Maximilian Stahlberg}, journal = {Journal of Open Source Software}, title = {{PICOS}: A {Python} interface to conic optimization solvers}, year = {2022}, issn = {2475-9066}, month = feb, number = {70}, pages = {3915}, volume = {7}, doi = {10.21105/joss.03915}, }

If citing a specific version of PICOS is necessary, then we offer also source deposits on Zenodo <https://doi.org/10.5281/zenodo.6052843>_.

License

PICOS is free and open source software and available to you under the terms of the GNU GPL v3 <https://gitlab.com/picos-api/picos/raw/master/LICENSE.txt>_.