Add recipe for getting infeasible constraints

[Joao-Dionisio]

Adds slack variables to the constraints and minimizes their sum. Non-zero slack variables correspond to infeasible constraints.

This is still far from Gurobi's Irreducible Inconsistent Subsystem. Take the following constraints:

x <= 3
x <= 4
x <= 5
x == 7

This function would return $4$ infeasible constraints, even though it is natural to take x == 7 as the constraint yielding the infeasibility.

Fix #855

[Opt-Mucca]

As I said in the meeting: My suggestion is to add an option to attach a binary variable to each slack variable. If the slack variable is non-zero then force the binary to 1 and minimise the sum of binaries. (This is going to be a behemoth of a model to solve, but would give a minimum amount of constraints that are forced to be invalid).

[Joao-Dionisio]

Thanks for the review @Opt-Mucca, I think it's done now.

The logical constraint was a bit more complicated than I realized, so I turned to OR SE (https://or.stackexchange.com/q/12142/5352) and implemented Erwin Kalvelagen's answer (who gracefully allowed me to use it).

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 30 lines in your changes missing coverage. Please review.

Project coverage is 52.29%. Comparing base (19b3ec9) to head (23e00b3).
Report is 1 commits behind head on master.

❗ Current head 23e00b3 differs from pull request most recent head 6b886e8

Please upload reports for the commit 6b886e8 to get more accurate results.

Files	Patch %	Lines
src/pyscipopt/recipes/infeasibilities.py	0.00%	30 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #857      +/-   ##
==========================================
- Coverage   52.53%   52.29%   -0.25%     
==========================================
  Files          19       20       +1     
  Lines        3961     3991      +30     
==========================================
+ Hits         2081     2087       +6     
- Misses       1880     1904      +24     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[Opt-Mucca]

Can you answer or resolve the older questions?

Two points for the current state:

• Why do you need the binary variables? They are created but never used, only the aux_binaries are.
• Make sure to remove the old objective function, otherwise you won't get an honest answer on the number of infeasible constraints.

[Joao-Dionisio]

@Opt-Mucca the binary variables are used in line 30. The formulation is not trivial, that's why I point to https://or.stackexchange.com/q/12142/5352. I need both binary and aux_binary in order to use SOS1 constraints.

Oops! Good catch on the objective function Mark.

[Joao-Dionisio]

I think that's it @Opt-Mucca!

[Opt-Mucca]

Am happy after our discussion!