sage-numerical-interactive-mip: Interactive mixed integer linear programming solver

This package is an extension of SageMath's mixed integer linear programming facilities described at http://doc.sagemath.org/html/en/reference/numerical/index.html

It was written by Peijun Xiao, Zeyi Wang, and Yuan Zhou in 2015-2016 at UC Davis for integration into SageMath.

Parts of their work (improvements to sage.numerical.interactive_simplex_method and MIP backend methods) that required changes to existing SageMath modules have already been integrated into SageMath in various tickets, see meta-ticket https://trac.sagemath.org/ticket/20302 (“Interactions with InteractiveLinearProgram and its dictionaries”).

The module sage_numerical_interactive_mip.interactive_milp_problem, written by Peijun Xiao, provides the interactive MILP problem classes, MILP tableau classes, and the cutting plane method. It is based on commit 5a4e3508d95e95e4491efcb2cf16fbe25be60bec, dated August 24, 2016, from the SageMath tree https://github.com/pgxiao/cutting-plane-method; this work superseded an earlier effort (adding integer variables in interactive_simplex_method) at https://trac.sagemath.org/ticket/18805

The modules sage_numerical_interactive_mip.clean_dictionary and sage_numerical_interactive_mip.backends.*_backend_dictionary, written by Zeyi (Aedi) Wang, provide a textbook view on a simplex basis in a numerical solver. They are based on https://trac.sagemath.org/ticket/18804

The branches were rebased by Matthias Koeppe in January 2020 onto SageMath version 9.1.beta1, then filtered using git filter-repo and merged.

How to use

This package uses the modularized distributions of portions of the Sage library provided by the passagemath project. No installation of SageMath is required. Just install the package with pip and start using it:

$ pip install sage-numerical-interactive-mip

$ ipython

In [1]: from sage_numerical_interactive_mip import *

In [2]: A = ([1, 1], [3, 1])

In [3]: b = (1000, 1500)

In [4]: c = (10, 5)

In [5]: P = InteractiveMILPProblem(A, b, c, ["C", "B"], variable_type=">=", integer_variables=True)

In [6]: P

The code comes with extensive documentation and tests; see the docstrings in the modules.

How to run the testsuite and build the HTML documentation

Install tox with pip, then run tox.

This also builds the documentation in .tox/docs/tmp/html/index.html.