[DNMY] Add MOI wrapper for CCOpt

[frapac]

With this PR, we can solve a JuMP model with complementarity constraints using CCOpt:

using JuMP
using CCOpt
using MathOptComplements
using NLPModelsJuMP

function fletcher_leyffer_ex2_model()
    model = Model()
    @variable(model, z[1:2] >= 0)
    @objective(model, Min, z[1] + z[2])
    @constraint(model, z[2]^2 >= 1)
    @constraint(model, [z[1], z[2]] ∈ MOI.Complements(2))
    return model
end


model = fletcher_leyffer_ex2_model()
MathOptComplements.Bridges.add_all_bridges(model)
set_optimizer(model, CCOpt.Optimizer)
JuMP.optimize!(model)

The MOI wrapper is developed as a package extension. It requires MathOptComplements to reformulate automatically the mixed-complementarity constraints in MOI as strict complementarity.

cc @blegat

[noahrhodes]

Is this branch fully working? It would be great for a current project

[apozharski]

Minor comments, and needs a rebase, but otherwise LGTM.

[apozharski]

I am not actually sure what this is supposed to return, but I should be return UNKNOWN_RESULT_STATUS?

[apozharski]

I guess this needs a rename.

[apozharski]

Advise perhaps MadNLP 😄

[apozharski]

@noahrhodes Hmmm I am not an MOI/JuMP expert 😅 (and I forgot that you actually asked for review on this, sorry @frapac ) but from what I can tell it seems like it should work, but the best way to know would be for someone to test it.