MixedIntegerLinearProgram backend using polymake (for LP over quadratic extensions) #22724
Description
polymake has a simple implementation of the dual simplex method, which works with polymake's quadratic extensions.
It appears to be much faster than our InteractiveLPbackend. It is unknown (because no benchmarking has been done) how much of the speed differential is due to InteractiveLP latexing all intermediate tableaux.
We should make it available as a MixedIntegerLinearProgram backend. (Of course, there are no integer variables.)
This could be based directly on
- Create a Polymake pexpect interface #22452: Create a polymake pexpect interface
or use - backend_polymake for Polyhedron #22683: backend_polymake for Polyhedron
See also: #22710: Meta-ticket: polymake
Depends on #22452
Component: numerical
Keywords: polymake
Issue created by migration from https://trac.sagemath.org/ticket/22724