add additional tests

Author: frapac

src/nonlinear.jl

@@ -204,7 +204,7 @@ function _relax_complementarity_upper_bound!(
 )
     lb1, ub1 = MOIU.get_bounds(model, Float64, x1)
     if isinf(ub1)
-        MOI.add_constraint(model, x1, MOI.GreaterThan(0.0))
+        MOI.add_constraint(model, x1, MOI.LessThan(0.0))
     else
         @assert ub1 == 0.0 # ensure we follow MOI's convention
         # TODO: what should we do if lb1 is finite?
@@ -379,7 +379,7 @@ function _relax_complementarity_upper_bound!(
 )
     lb1, ub1 = MOIU.get_bounds(model, Float64, x1)
     if isinf(ub1)
-        MOI.add_constraint(model, x1, MOI.GreaterThan(0.0))
+        MOI.add_constraint(model, x1, MOI.LessThan(0.0))
     else
         @assert ub1 == 0.0 # ensure we follow MOI's convention
         # TODO: what should we do if lb1 is finite?

test/runtests.jl

@@ -21,25 +21,66 @@ function fletcher_leyffer_ex1_nonlinear_model()
     return model
 end
 
-function nonlinear_test_model()
+function nonlinear_test_reformulated_model()
     model = Model()
     @variable(model, x >= 0.0)
     @variable(model, y >= 0.0)
+    @variable(model, slack >= 0)
     @objective(model, Min, x^2 + y^2 - 4*x*y)
     # Build complementarity constraints with nonlinear expression
-    @constraint(model, [sin(x), y] ∈ MOI.Complements(2))
+    @constraint(model, sin(x) == slack)
+    @constraint(model, slack * y <= 0.0)
     return model
 end
 
-function nonlinear_test_reformulated_model()
+function simple_ncp()
+    model = Model()
+    @variable(model, y <= 0)
+    @constraint(model, y + 1 ⟂ y)
+    return model, [y], [-1.0]
+end
+
+# Solve min_x x subject to 0 <= x <= 1
+function simple_lp_1()
+    model = Model()
+    @variable(model, 0 <= x <= 1)
+    @variable(model, μ)
+    @constraint(model, 1 - μ == 0.0)
+    @constraint(model, μ ⟂ x)
+    return model, [x, μ], [0.0, 1.0]
+end
+
+# Solve min_x -x subject to 0 <= x <= 1
+function simple_lp_2()
+    model = Model()
+    @variable(model, 0 <= x <= 1)
+    @variable(model, μ)
+    @constraint(model, -1 - μ == 0.0)
+    @constraint(model, μ ⟂ x)
+    return model, [x, μ], [1.0, -1.0]
+end
+
+# Solve min -x2 subject to (x1, x2) >= 0; x1 + x2 = 1
+function simple_lp_3()
+    model = Model()
+    @variable(model, 0.0 <= x[1:2])
+    @variable(model, 0.0 <= z[1:2])
+    @variable(model, y)
+    @constraint(model, -z[1] + y == 0.0)
+    @constraint(model, -1.0 - z[2] + y == 0.0)
+    @constraint(model, x[1] + x[2] == 1.0)
+    @constraint(model, z[1] ⟂ x[1])
+    @constraint(model, z[2] ⟂ x[2])
+    return model, [x; z; y], [0.0, 1.0, 1.0, 0.0, 1.0]
+end
+
+function nonlinear_test_model()
     model = Model()
     @variable(model, x >= 0.0)
     @variable(model, y >= 0.0)
-    @variable(model, slack >= 0)
     @objective(model, Min, x^2 + y^2 - 4*x*y)
     # Build complementarity constraints with nonlinear expression
-    @constraint(model, sin(x) == slack)
-    @constraint(model, slack * y <= 0.0)
+    @constraint(model, [sin(x), y] ∈ MOI.Complements(2))
     return model
 end
 
@@ -100,8 +141,17 @@ function test_nonlinear_mispecified_1()
     return model
 end
 
-# RHS is unbounded
+# LHS has a non-trivial upper-bound
 function test_nonlinear_mispecified_2()
+    model = Model()
+    @variable(model, x1 <= 1.0)
+    @variable(model, y1 <= 0.0)
+    @constraint(model, [x1, y1] ∈ MOI.Complements(2))
+    return model
+end
+
+# RHS is unbounded
+function test_nonlinear_mispecified_3()
     model = Model()
     @variable(model, x1)
     @variable(model, y1)
@@ -147,23 +197,12 @@ end
     @test_throws Exception MOI.Utilities.attach_optimizer(model)
 end
 
-@testset "Nonlinear reformulation $(relax)" for relax in [
+@testset "Nonlinear reformulation with $(relax)" for relax in [
     ComplementOpt.ScholtesRelaxation(0.0),
     ComplementOpt.FischerBurmeisterRelaxation(1e-8),
     ComplementOpt.LiuFukushimaRelaxation(1e-8),
     ComplementOpt.KanzowSchwarzRelaxation(1e-8),
 ]
-    model = test_nonlinear_reformulation()
-    set_optimizer(model, () -> ComplementOpt.Optimizer(Ipopt.Optimizer()))
-    MOI.set(model, ComplementOpt.RelaxationMethod(), relax)
-    MOI.Utilities.attach_optimizer(model)
-
-    for test_func in (test_nonlinear_mispecified_1, test_vertical_mispecified_2)
-        model = test_func()
-        set_optimizer(model, () -> ComplementOpt.Optimizer(Ipopt.Optimizer()))
-        MOI.set(model, ComplementOpt.RelaxationMethod(), relax)
-        @test_throws Exception MOI.Utilities.attach_optimizer(model)
-    end
 end
 
 instances = filter(names(Instances; all = true)) do name
@@ -180,22 +219,71 @@ end
     test_nonlinear_expr()
 end
 
-@testset "Relaxation method $(relax)" for relax in [
+@testset "Relaxation method: $(relax)" for relax in [
     ComplementOpt.ScholtesRelaxation(0.0),
     ComplementOpt.FischerBurmeisterRelaxation(1e-8),
     ComplementOpt.LiuFukushimaRelaxation(1e-8),
     ComplementOpt.KanzowSchwarzRelaxation(1e-8),
 ]
-    model = Instances.fletcher_leyffer_ex1_model()
-
-    JuMP.set_optimizer(model, () -> ComplementOpt.Optimizer(Ipopt.Optimizer()))
-    MOI.set(model, ComplementOpt.RelaxationMethod(), relax)
-    # Need to set the bound relaxation explicitly to 0 for LiuFukushimaRelaxation
-    JuMP.set_optimizer_attribute(model, "bound_relax_factor", 0.0)
-    JuMP.set_silent(model)
-    JuMP.optimize!(model)
-
-    @test JuMP.is_solved_and_feasible(model)
-    @test JuMP.objective_value(model) ≈ 0.5 atol=1e-7
-    @test JuMP.value.(model[:z]) ≈ [0.5, 0.5] atol=1e-7
+    @testset "Test reformulation" begin
+        model = test_nonlinear_reformulation()
+        set_optimizer(model, () -> ComplementOpt.Optimizer(Ipopt.Optimizer()))
+        MOI.set(model, ComplementOpt.RelaxationMethod(), relax)
+        MOI.Utilities.attach_optimizer(model)
+
+        for test_func in (
+            test_nonlinear_mispecified_1,
+            test_nonlinear_mispecified_2,
+            test_nonlinear_mispecified_3,
+        )
+            model = test_func()
+            set_optimizer(model, () -> ComplementOpt.Optimizer(Ipopt.Optimizer()))
+            MOI.set(model, ComplementOpt.RelaxationMethod(), relax)
+            @test_throws Exception MOI.Utilities.attach_optimizer(model)
+        end
+    end
+
+    @testset "Solve Fletcher-Leyffer Ex1 problem" begin
+        model = Instances.fletcher_leyffer_ex1_model()
+        JuMP.set_optimizer(model, () -> ComplementOpt.Optimizer(Ipopt.Optimizer()))
+        MOI.set(model, ComplementOpt.RelaxationMethod(), relax)
+        JuMP.set_optimizer_attribute(model, "bound_relax_factor", 0.0)
+        JuMP.set_silent(model)
+        JuMP.optimize!(model)
+
+        @test JuMP.is_solved_and_feasible(model)
+        @test JuMP.objective_value(model) ≈ 0.5 atol=1e-7
+        @test JuMP.value.(model[:z]) ≈ [0.5, 0.5] atol=1e-7
+    end
+
+    @testset "Solve NCP problem $(func)" for func in [simple_ncp, simple_lp_3]
+        model, vars, sol = func()
+        JuMP.set_optimizer(model, () -> ComplementOpt.Optimizer(Ipopt.Optimizer()))
+        MOI.set(model, ComplementOpt.RelaxationMethod(), relax)
+        JuMP.set_optimizer_attribute(model, "bound_relax_factor", 0.0)
+        JuMP.set_silent(model)
+        JuMP.optimize!(model)
+
+        @test JuMP.is_solved_and_feasible(model)
+        @test JuMP.value.(vars) ≈ sol atol=1e-7
+    end
+end
+
+# N.B.: at the moment, mixed-complementarity problems are supported only
+# with ScholtesRelaxation and with FischerBurmeisterRelaxation
+@testset "Mixed-complementarity problem with $(relax)" for relax in [
+    ComplementOpt.ScholtesRelaxation(0.0),
+    ComplementOpt.FischerBurmeisterRelaxation(1e-8),
+]
+    @testset "Solve NCP problem $(func)" for func in [simple_lp_1, simple_lp_2]
+        model, vars, sol = func()
+        JuMP.set_optimizer(model, () -> ComplementOpt.Optimizer(Ipopt.Optimizer()))
+        MOI.set(model, ComplementOpt.RelaxationMethod(), relax)
+        JuMP.set_optimizer_attribute(model, "bound_relax_factor", 0.0)
+        JuMP.set_silent(model)
+        JuMP.optimize!(model)
+
+        @test JuMP.is_solved_and_feasible(model)
+        @test JuMP.value.(vars) ≈ sol atol=1e-7
+    end
 end