rethink MIP callbacks (from scratch)

[chriscoey]

to be discussed at the meetup

see https://github.com/JuliaOpt/MathProgBase.jl/issues/16 for discussion of branching and incumbent callbacks

[ccoffrin]

An attempt collect solver callback documentation.

Significant Callback Support

• Gurobi
• CPlex
• SCIP
• Express
• Mosek
• Knitro
• GLPK (in PDF available here)

Minor/Unclear Callback Support

• Ipopt
• Bonmin

[ccoffrin]

Notes from meetup discussion,

• we will not attempt to generalize over callbacks, there is too much diversity in the solvers
• we should try to design a clean callback architecture pattern for users working at the MPB level
• Cplex.jl's dependency on JuMP for implementing callbacks is undesirable
• a good test of the any proposed architecture is an approach that can work for SCIP.jl, Cplex.jl, and Guorbi.jl
• lack of clarity about what is going on at the JuMP level is undesirable for example,
  • what is the cb object?
  • what is the semantics of @lazyconstraint?

[mlubin]

More discussions with @chriscoey: don't port over callbacks to the new API until we have a first pass of the JuMP implementation. At that point we can reevaluate if we should port them over or design a new API.