Meta-ticket: Improvements to MixedIntegerLinearProgram and its backends

[Matthias Köppe]

Frontend:

• #20304: More error checking in MixedIntegerLinearProgram
• #19523: defect: Adding constraints for the wrong MILP crashes Sage
• #18733: enhancement: MixedIntegerLinearProgram should support tableau-query methods
• #18688: task: MixedIntegerLinearProgram should support basis status getting/setting

Improvements to backends:

• #20303: Fixes for add_variables in CVXOPT, PPL, GLPK MIP backends and add_linear_constraints in CVXOPT
• #19525: enhancement: Improve GLPK error handling
• #20323: Common TestSuite for MIP backends
• #20324: MIP backends: Unify add_col, add_variable
• #20325: GenericBackend: Add default implementation of add_variables and add_linear_constraints
• #20326: GenericBackend: Fix doctest of add_linear_constraint_vector
• #20328: tests related to cplex / gurobi

New backends:

• #20296: MixedIntegerLinearProgram: New backend using InteractiveLPProblem
• #18735: MixedIntegerLinearProgram/HybridBackend: Reconstruct exact rational/algebraic basic solution
• #19219: MILP: Add "CyLP" backend
• #18862: Interface to COIN OpenSolverInterface
• #8672 SCIP support
• #10879: add optional SCIP integer constraint solver
• #18766: Add bindings, MixedIntegerLinearProgram backend to qsopt_ex, a state-of-the-art exact simplex solver

Interactions with InteractiveLinearProgram and its dictionaries:

• #18734: Construct an interactive_simplex_method.LPDictionary from a MixedIntegerLinearProgram
• #20311: interactive_simplex_method enhancements
• #20203: LPCleanDictionary - floating-point helper class for interactive simplex method
• #18804: LPBackendDictionary - a debugging view of a MIP backend connected to interactive_simplex_method

Interactions with polyhedra:

• #20301 Polyhedron.to_linear_program should return the MIP variable used

[Matthias Köppe]

Description modified to remove my comments about variable_upper_bound and variable_lower_bound. I was misled by the interface description in GenericBackend, which was out of sync with the real backends. Fixed in #20296

[Vincent Delecroix]

Hello,

I guess that you do not want to fix all of that in one ticket. One possibility is to use this one as a "task ticket" pointing to other tickets. See for example #18846, #17601 or #18333.