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add more tests, in particular for dual variables, cf. #290 (#332)
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* add more tests, in particular for dual variables, cf. #290

* add tests of dual problem value for minimum norm problems

* fix typo in dual test
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@ranocha @ericphanson
ranocha authored and ericphanson committed Oct 13, 2019
1 parent 8ec3be8 commit e0513ac
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Showing 2 changed files with 87 additions and 2 deletions.
22 changes: 22 additions & 0 deletions test/test_lp.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -6,13 +6,25 @@
solve!(p, solver)
@test p.optval ≈ 1 atol=TOL
@test evaluate(abs(x)) ≈ 1 atol=TOL
if p.solution.has_dual
println("Solution object has dual value, checking for dual correctness.")
@test p.constraints[1].dual ≈ 1 atol=TOL
end

x = Variable(2,2)
p = minimize(sum(abs(x)), x[2,2]>=1, x[1,1]>=1, x>=0)
@test vexity(p) == ConvexVexity()
solve!(p, solver)
@test p.optval ≈ 2 atol=TOL
@test evaluate(sum(abs(x))) ≈ 2 atol=TOL
if p.solution.has_dual
println("Solution object has dual value, checking for dual correctness.")
@test p.constraints[1].dual ≈ 1 atol=TOL
@test p.constraints[2].dual ≈ 1 atol=TOL
@test p.constraints[3].dual[1,1] ≈ 0 atol=TOL
@test p.constraints[3].dual[2,2] ≈ 0 atol=TOL
@test p.constraints[3].dual[1,2] ≈ p.constraints[3].dual[2,1] atol=TOL
end
end

@testset "maximum atom" begin
Expand Down Expand Up @@ -155,6 +167,11 @@
solve!(p, solver)
@test p.optval ≈ 0 atol=TOL
@test evaluate(norm_inf(x)) ≈ 0 atol=TOL
if p.solution.has_dual
println("Solution object has dual value, checking for dual correctness.")
@test norm(p.constraints[1].dual) ≈ 0 atol=TOL
@test norm(p.constraints[2].dual) ≈ 0 atol=TOL
end
end

@testset "norm 1 atom" begin
Expand All @@ -164,5 +181,10 @@
solve!(p, solver)
@test p.optval ≈ 0 atol=TOL
@test evaluate(norm_1(x)) ≈ 0 atol=TOL
if p.solution.has_dual
println("Solution object has dual value, checking for dual correctness.")
@test norm(p.constraints[1].dual) ≈ 0 atol=TOL
@test norm(p.constraints[2].dual) ≈ 0 atol=TOL
end
end
end
67 changes: 65 additions & 2 deletions test/test_socp.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -19,15 +19,23 @@
solve!(p, solver)
@test p.optval ≈ 14.9049 atol=TOL
@test evaluate(norm2(A * x + b) + lambda * norm2(x)) ≈ 14.9049 atol=TOL
if p.solution.has_dual
println("Solution object has dual value, checking for dual correctness.")
dual = [4.4134, 5.1546]
@test p.constraints[1].dual ≈ dual atol=TOL
end

x = Variable(2)

p = minimize(norm2([x[1] + 2x[2] + 2; 2x[1] + x[2] + 3; 3x[1]+4x[2] + 4]) + lambda * norm2(x), x >= 1)
@test vexity(p) == ConvexVexity()

solve!(p, solver)
@test p.optval ≈ 14.9049 atol=TOL
@test evaluate(norm2(A * x + b) + lambda * norm2(x)) ≈ 14.9049 atol=TOL
if p.solution.has_dual
println("Solution object has dual value, checking for dual correctness.")
dual = [4.4134, 5.1546]
@test p.constraints[1].dual ≈ dual atol=TOL
end

x = Variable(2, 1)
A = [1 2; 2 1; 3 4]
Expand All @@ -38,6 +46,11 @@
solve!(p, solver)
@test p.optval ≈ 15.4907 atol=TOL
@test evaluate(norm2(A * x + b) + lambda * norm_1(x)) ≈ 15.4907 atol=TOL
if p.solution.has_dual
println("Solution object has dual value, checking for dual correctness.")
dual = [4.7062, 5.4475]
@test p.constraints[1].dual ≈ dual atol=TOL
end
end

@testset "frobenius norm atom" begin
Expand All @@ -48,6 +61,12 @@
solve!(p, solver)
@test p.optval ≈ sqrt(35) atol=TOL
@test evaluate(norm(vec(m), 2)) ≈ sqrt(35) atol=TOL
if p.solution.has_dual
println("Solution object has dual value, checking for dual correctness.")
@test p.constraints[1].dual ≈ 0.6761 atol=TOL
dual = 0.1690 .* ones(4, 5); dual[3, 3] = 0
@test p.constraints[2].dual ≈ dual atol=TOL
end
end

@testset "quad over lin atom" begin
Expand Down Expand Up @@ -277,5 +296,49 @@
@test o1 <= o2
end
end

@testset "minimal norm solutions" begin
x = Variable(2)
A = [1 2; 2 4];
b = [3, 6];
p = minimize(norm(x, 1), A*x==b)
@test vexity(p) == ConvexVexity()
solve!(p, solver)
@test p.optval ≈ 1.5 atol=TOL
@test evaluate(x) ≈ [0, 1.5] atol=TOL
@test evaluate(norm(x, 1)) ≈ p.optval atol=TOL
if p.solution.has_dual
println("Solution object has dual value, checking for dual problem correctness.")
@test dot(b, p.constraints[1].dual) ≈ p.optval atol=TOL
end

x = Variable(2)
A = [1 2; 2 4];
b = [3, 6];
p = minimize(norm(x, 2), A*x==b)
@test vexity(p) == ConvexVexity()
solve!(p, solver)
@test p.optval ≈ 3/sqrt(5) atol=TOL
@test evaluate(x) ≈ [3/5, 6/5] atol=TOL
@test evaluate(norm(x, 2)) ≈ p.optval atol=TOL
if p.solution.has_dual
println("Solution object has dual value, checking for dual problem correctness.")
@test dot(b, p.constraints[1].dual) ≈ p.optval atol=TOL
end

x = Variable(2)
A = [1 2; 2 4];
b = [3, 6];
p = minimize(norm(x, Inf), A*x==b)
@test vexity(p) == ConvexVexity()
solve!(p, solver)
@test p.optval ≈ 1.0 atol=TOL
@test evaluate(x) ≈ [1, 1] atol=TOL
@test evaluate(norm(x, Inf)) ≈ p.optval atol=TOL
if p.solution.has_dual
println("Solution object has dual value, checking for dual problem correctness.")
@test dot(b, p.constraints[1].dual) ≈ p.optval atol=TOL
end
end
end
end

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