MILP: Add CyLP backend

[mkoeppe]

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

[nathanncohen]

comment:1

I don't have anything against what you plan to do, but why exactly do you want to add a CyLP backend? It may be true that CyLP has more features exposed than our current interface, but then the same thing remains: in the backend, you will have to expose the features that are exposed in CyLP, exactly how we have to do now by exposing in the coin backend the features that are exposed in the C++ Api.

Nathann

[dimpase]

comment:2

Matthias builds a database of ILP cutting planes constructions (Actually I talked to him yesterday about it at length).

He wants his cuts to be as painless as possible:)