Unboundness master idea

[IainNZ]

In the event the master is unbounded, we'll have a ray and a feasible solution (I think thats what we get, or can get - need to look into this)

So the cutting plane problem is now

• for a constraint u^T x <= b
• given feasible y and ray r
• find a u and s such that u^T (y + s*r) > b
• but its actually much easier than that - you just need to find a u such that u^T r > 0 because then you just scale s

So thats, mathematically, how you do it. But working this into the oracle interface is a bit more painful. A fallback would be just setting s to a biggish-M - better than the box at least.

[IainNZ]

No choice essentially but to punt on this, because its a MIP, Gurobi will declare unboundedness without even checking the cutting planes. Actually, even worse, it does for the heuristic, but doesn't add them to the master.

The solution: add a add_box option to add a box only if user wants it.

Todo:

• document, and
• maybe make a warning in _solve_robust if unbounded is that status.