Considers constrained variables from Dualization

[joaquimg]

Since #171 the latest Dualization is supported.
Additional changes are required to support compact for of dual because more data has to be read from PrimalDualMap.

[LukasBarner]

What needs to be done on this end?
I think this should greatly decrease solution times for problems with many variable bounds...
For quite a few examples, it already seems to work fine.
Some of the tests still seem to fail, but this may also be for other reasons...

[joaquimg]

I am not 100% sure this will change considerably the solution times.

Right now, BilevelJuMP is only able to write a KKT from a Dualization.jl Standard form.
To support this, we need to be able to handle Compact form.
The main missing piece is the second complementarity condition in: https://jump.dev/Dualization.jl/dev/manual/#KKT-3
but there is some bookkeeping to be done around.

[LukasBarner]

So it would be required to add complements for the inequality stationarity conditions related to primal bounded variables, right? My guess that this would speed things up was because one dual variable per bound could actually be cut out then

[LukasBarner]

Think I may have found a way for this without too much unnecessary bookkeeping: #189.
Relevant are only the last three commits (the rest is the iterative stuff, just wanted to make sure it also works for that..).
Do you think this might be worth further efforts?

[LukasBarner]

PS: sorry for the spam here and on Dualization.jl the last few days :D