Implement main nonlinear reformulations for complementarity constraints (#9)

* implement main nonlinear reformulations for complementarity constraints

* fix CI

* fix formulation of Fischer-Burmeister relaxation

* Relax tol

* Fix test

---------

Co-authored-by: Benoît Legat <benoit.legat@gmail.com>

Author: frapac

src/ComplementOpt.jl

@@ -3,6 +3,7 @@ module ComplementOpt
 using JuMP
 const MOIU = MOI.Utilities
 
+include("utils.jl")
 include("vertical.jl")
 include("nonlinear.jl")
 include("MOI_wrapper.jl")

src/MOI_wrapper.jl

@@ -2,11 +2,11 @@ struct Reformulation <: MOI.AbstractOptimizerAttribute end
 
 struct Optimizer{O<:MOI.ModelLike} <: MOI.AbstractOptimizer
     optimizer::O
-    reformulation
+    reformulation::AbstractComplementarityRelaxation
     function Optimizer(optimizer::MOI.ModelLike)
         return new{typeof(optimizer)}(
             optimizer,
-            NonlinearReformulation(),
+            ScholtesRelaxation(0.0),
         )
     end
 end
@@ -59,7 +59,7 @@ function MOI.copy_to(dest::Optimizer, src::MOI.ModelLike)
     )
     tmp_index_map = MOI.copy_to(tmp, src)
     reformulate_to_vertical!(tmp)
-    reformulate_as_nonlinear_program!(tmp)
+    reformulate_as_nonlinear_program!(tmp, dest.reformulation)
     # TODO combine with `tmp_index_map`
     return MOI.copy_to(dest.optimizer, tmp)
 end