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Merged
odow merged 3 commits into from
Oct 10, 2019
Merged

Add QP complementarity test #918

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d9be71d
Test: add QP complementarity test
frapac Oct 9, 2019
8fc7f4d
Add Mock test for QP complementarity test
frapac Oct 10, 2019
667f930
Fix with comments in PR#918
frapac Oct 10, 2019
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102 changes: 97 additions & 5 deletions src/Test/nlp.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -371,16 +371,108 @@ function test_linear_mixed_complementarity(model::MOI.ModelLike, config::TestCon
MOI.Complements(4)
)
@test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
MOI.optimize!(model)
@test MOI.get(model, MOI.TerminationStatus()) == config.optimal_status
x_val = MOI.get.(model, MOI.VariablePrimal(), x)
@test isapprox(
x_val, [2.8, 0.0, 0.8, 1.2], atol = config.atol, rtol = config.rtol
if config.solve
MOI.optimize!(model)
@test MOI.get(model, MOI.TerminationStatus()) == config.optimal_status
x_val = MOI.get.(model, MOI.VariablePrimal(), x)
@test isapprox(
x_val, [2.8, 0.0, 0.8, 1.2], atol = config.atol, rtol = config.rtol
)
end
end

"""
test_qp_mixed_complementarity(model::MOI.ModelLike, config::TestConfig)

Test the solution of the quadratic mixed-complementarity problem:

```
min (x0 - 5)^2 +(2 x1 + 1)^2
s.t. -1.5 x0 + 2 x1 + x2 - 0.5 x3 + x4 = 2
x2 complements(3 x0 - x1 - 3)
x3 complements(-x0 + 0.5 x1 + 4)
x4 complements(-x0 - x1 + 7)
x0, x1, x2, x3, x4 >= 0

```
which rewrites, with auxiliary variables

```
min (x0 - 5)^2 +(2 x1 + 1)^2
s.t. -1.5 x0 + 2 x1 + x2 - 0.5 x3 + x4 = 2 (cf1)
3 x0 - x1 - 3 - x5 = 0 (cf2)
-x0 + 0.5 x1 + 4 - x6 = 0 (cf3)
-x0 - x1 + 7 - x7 = 0 (cf4)
x2 complements x5
x3 complements x6
x4 complements x7
x0, x1, x2, x3, x4, x5, x6, x7 >= 0

```
"""
function test_qp_mixed_complementarity(model::MOI.ModelLike, config::TestConfig)
MOI.empty!(model)
x = MOI.add_variables(model, 8)
MOI.set.(model, MOI.VariablePrimalStart(), x, 0.0)
for i in 1:8
MOI.add_constraint(model, MOI.SingleVariable(x[i]), MOI.GreaterThan(0.0))
end

obj = MOI.ScalarQuadraticFunction(
[MOI.ScalarAffineTerm(-10.0, x[1]), MOI.ScalarAffineTerm(4.0, x[2])],
[MOI.ScalarQuadraticTerm(2.0, x[1], x[1]), MOI.ScalarQuadraticTerm(8.0, x[2], x[2])],
26.0)

MOI.set(model, MOI.ObjectiveFunction{MOI.ScalarQuadraticFunction{Float64}}(), obj)

cf1 = MOI.ScalarAffineFunction([
MOI.ScalarAffineTerm(-1.5, x[1]),
MOI.ScalarAffineTerm(2.0, x[2]),
MOI.ScalarAffineTerm(1.0, x[3]),
MOI.ScalarAffineTerm(0.5, x[4]),
MOI.ScalarAffineTerm(1.0, x[5])
], 0.0)
cf2 = MOI.ScalarAffineFunction([
MOI.ScalarAffineTerm(3.0, x[1]),
MOI.ScalarAffineTerm(-1.0, x[2]),
MOI.ScalarAffineTerm(-1.0, x[6]),
], 0.0)
cf3 = MOI.ScalarAffineFunction([
MOI.ScalarAffineTerm(-1.0, x[1]),
MOI.ScalarAffineTerm(0.5, x[2]),
MOI.ScalarAffineTerm(-1.0, x[7]),
], 0.0)
cf4 = MOI.ScalarAffineFunction([
MOI.ScalarAffineTerm(-1.0, x[1]),
MOI.ScalarAffineTerm(-1.0, x[2]),
MOI.ScalarAffineTerm(-1.0, x[8]),
], 0.0)

MOI.add_constraint(model, cf1, MOI.EqualTo(2.0))
MOI.add_constraint(model, cf2, MOI.EqualTo(3.0))
MOI.add_constraint(model, cf3, MOI.EqualTo(-4.0))
MOI.add_constraint(model, cf4, MOI.EqualTo(-7.0))

MOI.add_constraint(
model,
MOI.VectorOfVariables([x[3], x[4], x[5], x[6], x[7], x[8]]),
MOI.Complements(3)
)
@test MOI.get(model, MOI.TerminationStatus()) == MOI.OPTIMIZE_NOT_CALLED
if config.solve
MOI.optimize!(model)
@test MOI.get(model, MOI.TerminationStatus()) == config.optimal_status
x_val = MOI.get.(model, MOI.VariablePrimal(), x)
@test isapprox(
x_val, [1.0, 0.0, 3.5, 0.0, 0.0, 0.0, 3.0, 6.0], atol = config.atol, rtol = config.rtol
)
@test MOI.get(model, MOI.ObjectiveValue()) ≈ 17.0 atol=config.atol rtol=config.rtol
end
end

const complementaritytests = Dict(
"linear_mixed_complementarity" => test_linear_mixed_complementarity,
"qp_mixed_complementarity" => test_qp_mixed_complementarity,
)

@moitestset complementarity
8 changes: 8 additions & 0 deletions test/Test/nlp.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -16,4 +16,12 @@ const MOI = MathOptInterface
)
)
MOI.Test.test_linear_mixed_complementarity(mock, config)

MOI.Utilities.set_mock_optimize!(
mock,
(mock) -> MOI.Utilities.mock_optimize!(
mock, config.optimal_status, [1.0, 0.0, 3.5, 0.0, 0.0, 0.0, 3.0, 6.0]
)
)
MOI.Test.test_qp_mixed_complementarity(mock, config)
end