Reformulations fail basic cases

[odow]

This needs revisiting:

julia> using JuMP, Ipopt, MathOptComplements

julia> model = Model(() -> MathOptComplements.Optimizer(Ipopt.Optimizer()))
A JuMP Model
├ solver: Ipopt
├ objective_sense: FEASIBILITY_SENSE
├ num_variables: 0
├ num_constraints: 0
└ Names registered in the model: none

julia> @variable(model, x >= 1)
x

julia> @variable(model, y >= 0)
y

julia> @constraint(model, x ⟂ y)
[x, y] ∈ MathOptInterface.Complements(2)

julia> optimize!(model)
ERROR: AssertionError: lb1 == 0.0
Stacktrace:
  [1] _relax_complementarity_lower_bound!(model::MathOptComplements.Optimizer{…}, relaxation::MathOptComplements.Bridges.ScholtesRelaxation{…}, x1::MathOptInterface.VariableIndex, x2::MathOptInterface.VariableIndex, lb2::Float64, ub2::Float64)

It's a valid MCP

julia> using JuMP, PATHSolver

julia> model = Model(PATHSolver.Optimizer)
A JuMP Model
├ solver: Path 5.1.99
├ objective_sense: FEASIBILITY_SENSE
├ num_variables: 0
├ num_constraints: 0
└ Names registered in the model: none

julia> @variable(model, x >= 1)
x

julia> @variable(model, y >= 0)
y

julia> @constraint(model, x ⟂ y)
[x, y] ∈ MathOptInterface.Complements(2)

julia> optimize!(model)
Path 5.1.99 (Mon Jul 24 14:47:28 2023)
Written by Todd Munson, Steven Dirkse, Youngdae Kim, and Michael Ferris

Zero:     2 Single:     0 Double:     0

Major Iterations. . . . 0
Minor Iterations. . . . 0
Restarts. . . . . . . . 0
Crash Iterations. . . . 0
Gradient Steps. . . . . 0
Function Evaluations. . 0
Gradient Evaluations. . 0
Basis Time. . . . . . . 0.000000
Total Time. . . . . . . 0.000181
Residual. . . . . . . . 0.000000e+00
Postsolved residual: 0.0000e+00

julia> value(x), value(y)
(1.0, 0.0)

[odow]

Closing in favour of #66. I don't know what's going on with GitHub these days.