Trying multistage FWPH

[bknueven]

This runs. Questions:

1. Is the bound provided valid?
2. Is our implementation accidentally the multistage implementation?

[DLWoodruff]

Line 35 of straight_tests.py needs to have --no-fwph added to it (the alternative is to change -np 3 to -np 4 in the same line)

[dtmildebrath]

I don't suppose we have any other 3-stage IPs lying around? (I vaguely recall a forestry problem...?)

[dtmildebrath]

Skimmed back through the Boland paper. I would have to set pen to paper to be confident in this, but it seems more plausible to me now that this may be the multistage algorithm. However, as Ben as already raised, it's still possible that this is a weaker version that it might be. In any event, I'm about 90% convinced this should produce valid lower bounds for multistage problems. We are essentially still solving (9) from Boland--building an inner approximation to the convex hull of each scenario, etc.

[bknueven]

Doing my own review, I'm inclined to agree with @dtmildebrath. The only complicating part would be in computing xbar (or z in the Boland paper), but this is already handled by PHBase. The FWPH implementation we have separates the variables by non-leaf variables and leaf variables, which is exactly what it seems you would want to do for a multistage extension of this algorithm.

Therefore I've removed the warning when using FWPH with multistage, and I think this should be merged.