CyLP is a Cython interface to COIN-OR’s Linear and mixed-integer program solvers (CLP, CBC, and CGL).

We should add a MILP backend that goes through CyLP, because the interface is much more complete than Sage's current COIN interface. In particular, quoting from CyLP's README:

"CyLP’s unique feature is that you can use it to alter the solution process of the solvers from within Python. For example, you may define cut generators, branch-and-bound strategies, and primal/dual Simplex pivot rules completely in Python."

https://github.com/coin-or/CyLP

Of course, CyLP has an incompatible license (CPL), but it does not matter because COIN has that license already.

Update: CyLP has various outstanding issues (https://github.com/coin-or/CyLP/issues) that need working around or fixing

CC: @nathanncohen @dimpase

Component: numerical

Issue created by migration from https://trac.sagemath.org/ticket/19219