Duals edge case: no binaries in objective function

Suppose I have a system where every thermal has zero no-load cost, startup cost, shutdown cost, and Pmin. The binary variables u only appear only in the constraints (p ≤ Pmax·u and p ≥ 0·u) and nowhere in the objective. Hence UC and ED are the same problem.

However, process_duals fixes every binary at its MIP value and re-solves as an LP. The binaries are cost-free, so the optimizer picks an arbitrary vertex with many u = 0. The UC dual calculation pins a bunch of generators at p = 0, while the ED dual calculation leaves them free. Thus we get dramatically different values for duals. (AI says this is exacerbated by larger MIPRELSTOP values.)

This is an edge case...but it's still rather confusing. imo the minimum would be to add a warning, something like "[n] of [k] binary decision variables have arbitrary values." Maybe error if n equals k. The comprehensive fix would be to somehow address this degeneracy head-on.

(Found by @maitreyeemarathe)