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[Utilities] add support for relaxing vector constraints #2966

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odow merged 1 commit into from
Mar 10, 2026
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[Utilities] add support for relaxing vector constraints #2966

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46 changes: 45 additions & 1 deletion src/Utilities/penalty_relaxation.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -187,16 +187,60 @@ function _relax_constraint(
return [x]
end

function _slack_vector(set::MOI.AbstractVectorSet)
ret = Pair{Int,Int}[]
for i in 1:MOI.dimension(set)
push!(ret, i => +1)
push!(ret, i => -1)
end
return ret
end

_slack_vector(set::MOI.Nonnegatives) = [i => +1 for i in 1:MOI.dimension(set)]
_slack_vector(set::MOI.Nonpositives) = [i => -1 for i in 1:MOI.dimension(set)]
_slack_vector(::MOI.SecondOrderCone) = [1 => +1]
_slack_vector(::MOI.RotatedSecondOrderCone) = [1 => +1, 2 => +1]
_slack_vector(::MOI.NormOneCone) = [1 => +1]
_slack_vector(::MOI.NormInfinityCone) = [1 => +1]
_slack_vector(::MOI.NormCone) = [1 => +1]
_slack_vector(::MOI.NormSpectralCone) = [1 => +1]
_slack_vector(::MOI.NormNuclearCone) = [1 => +1]
_slack_vector(::MOI.RootDetConeTriangle) = [1 => -1]
_slack_vector(::MOI.LogDetConeTriangle) = [1 => -1, 2 => +1]

function _slack_vector(set::MOI.GeometricMeanCone)
ret = [i => +1 for i in 1:MOI.dimension(set)]
ret[1] = (1 => -1)
return ret
end

function _relax_constraint(
::Type{T},
model::MOI.ModelLike,
ci::MOI.ConstraintIndex{F,<:MOI.AbstractVectorSet},
) where {T,F<:Union{MOI.VectorAffineFunction{T},MOI.VectorQuadraticFunction{T}}}
set = MOI.get(model, MOI.ConstraintSet(), ci)
slack = _slack_vector(set)
y, _ = MOI.add_constrained_variables(model, MOI.Nonnegatives(length(slack)))
for (i, (row, weight)) in enumerate(slack)
change = MOI.MultirowChange(y[i], [(Int64(row), weight * one(T))])
MOI.modify(model, ci, change)
end
return y
end

function MOI.modify(
model::MOI.ModelLike,
ci::MOI.ConstraintIndex{F,<:MOI.AbstractScalarSet},
ci::MOI.ConstraintIndex{F},
relax::ScalarPenaltyRelaxation{T},
) where {
T,
F<:Union{
MOI.ScalarAffineFunction{T},
MOI.ScalarQuadraticFunction{T},
MOI.ScalarNonlinearFunction,
MOI.VectorAffineFunction{T},
MOI.VectorQuadraticFunction{T},
},
}
x = _relax_constraint(T, model, ci)
Expand Down
252 changes: 252 additions & 0 deletions test/Utilities/test_penalty_relaxation.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -475,6 +475,258 @@ function test_scalar_penalty_relaxation_vector_objective()
return
end

function test_relax_vector_epigraph_cones()
_test_roundtrip(
"""
variables: x, y, z
c1: [1.0 * x, y, z] in SecondOrderCone(3)
""",
"""
variables: x, y, z, a
minobjective: 1.0 * a
c1: [1.0 * x + 1.0 * a, y, z] in SecondOrderCone(3)
[a] in Nonnegatives(1)
""",
)
_test_roundtrip(
"""
variables: x, y, z
c1: [1.0 * x, y, z] in RotatedSecondOrderCone(3)
""",
"""
variables: x, y, z, a, b
minobjective: 1.0 * a + 1.0 * b
c1: [1.0 * x + 1.0 * a, y + 1.0 * b, z] in RotatedSecondOrderCone(3)
[a, b] in Nonnegatives(2)
""",
)
_test_roundtrip(
"""
variables: x, y, z
c1: [1.0 * x, y, z] in NormOneCone(3)
""",
"""
variables: x, y, z, a
minobjective: 1.0 * a
c1: [1.0 * x + 1.0 * a, y, z] in NormOneCone(3)
[a] in Nonnegatives(1)
""",
)
_test_roundtrip(
"""
variables: x, y, z
c1: [1.0 * x, y, z] in NormInfinityCone(3)
""",
"""
variables: x, y, z, a
minobjective: 1.0 * a
c1: [1.0 * x + 1.0 * a, y, z] in NormInfinityCone(3)
[a] in Nonnegatives(1)
""",
)
_test_roundtrip(
"""
variables: x, y, z
c1: [1.0 * x, y, z] in NormCone(1.5, 3)
""",
"""
variables: x, y, z, a
minobjective: 1.0 * a
c1: [1.0 * x + 1.0 * a, y, z] in NormCone(1.5, 3)
[a] in Nonnegatives(1)
""",
)
_test_roundtrip(
"""
variables: x, y, z
c1: [1.0 * x, y, z] in NormSpectralCone(1, 2)
""",
"""
variables: x, y, z, a
minobjective: 1.0 * a
c1: [1.0 * x + 1.0 * a, y, z] in NormSpectralCone(1, 2)
[a] in Nonnegatives(1)
""",
)
_test_roundtrip(
"""
variables: x, y, z
c1: [1.0 * x, y, z] in NormNuclearCone(1, 2)
""",
"""
variables: x, y, z, a
minobjective: 1.0 * a
c1: [1.0 * x + 1.0 * a, y, z] in NormNuclearCone(1, 2)
[a] in Nonnegatives(1)
""",
)
_test_roundtrip(
"""
variables: x, y, z
c1: [1.0 * x * x, 1.0 * y, 1.0 * z] in NormCone(1.5, 3)
""",
"""
variables: x, y, z, a
minobjective: 1.0 * a
c1: [1.0 * x * x + 1.0 * a, 1.0 * y, 1.0 * z] in NormCone(1.5, 3)
[a] in Nonnegatives(1)
""",
)
return
end

function test_relax_vector_hypograph_cones()
_test_roundtrip(
"""
variables: t, x, y, z
c1: [1.0 * t, x, y, z] in RootDetConeTriangle(2)
""",
"""
variables: t, x, y, z, a
minobjective: 1.0 * a
c1: [1.0 * t + -1.0 * a, x, y, z] in RootDetConeTriangle(2)
[a] in Nonnegatives(1)
""",
)
_test_roundtrip(
"""
variables: t, u, x, y, z
c1: [1.0 * t, u, x, y, z] in LogDetConeTriangle(2)
""",
"""
variables: t, u, x, y, z, a, b
minobjective: 1.0 * a + 1.0 * b
c1: [1.0 * t + -1.0 * a, u + 1.0 * b, x, y, z] in LogDetConeTriangle(2)
[a, b] in Nonnegatives(2)
""",
)
return
end

function test_relax_nonnegatives()
_test_roundtrip(
"""
variables: x, y
c1: [1.0 * x, y] in Nonnegatives(2)
""",
"""
variables: x, y, a, b
minobjective: 1.0 * a + 1.0 * b
c1: [1.0 * x + 1.0 * a, y + 1.0 * b] in Nonnegatives(2)
[a, b] in Nonnegatives(2)
""",
)
return
end

function test_relax_nonpositives()
_test_roundtrip(
"""
variables: x, y
c1: [1.0 * x, y] in Nonpositives(2)
""",
"""
variables: x, y, a, b
minobjective: 1.0 * a + 1.0 * b
c1: [1.0 * x + -1.0 * a, y + -1.0 * b] in Nonpositives(2)
[a, b] in Nonnegatives(2)
""",
)
return
end

function test_relax_geometric_mean_cone()
_test_roundtrip(
"""
variables: x, y, z
c1: [1.0 * x, y, z] in GeometricMeanCone(3)
""",
"""
variables: x, y, z, a, b, c
minobjective: 1.0 * a + 1.0 * b + 1.0 * c
c1: [1.0 * x + -1.0 * a, y + 1.0 * b, z + 1.0 * c] in GeometricMeanCone(3)
[a, b, c] in Nonnegatives(3)
""",
)
return
end

function test_relax_both_sides()
_test_roundtrip(
"""
variables: x, y
c1: [1.0 * x, y] in Zeros(2)
""",
"""
variables: x, y, a, b, c, d
minobjective: 1.0 * a + 1.0 * b + 1.0 * c + 1.0 * d
c1: [1.0 * x + 1.0 * a + -1.0 * b, y + 1.0 * c + -1.0 * d] in Zeros(2)
[a, b, c, d] in Nonnegatives(4)
""",
)
_test_roundtrip(
"""
variables: x, y, z
c1: [1.0 * x, y, z] in ExponentialCone()
""",
"""
variables: x, y, z, a, b, c, d, e, f
minobjective: 1.0 * a + 1.0 * b + 1.0 * c + 1.0 * d + 1.0 * e + 1.0 * f
c1: [1.0 * x + 1.0 * a + -1.0 * b, y + 1.0 * c + -1.0 * d, z + 1.0 * e + -1.0 * f] in ExponentialCone()
[a, b, c, d, e, f] in Nonnegatives(6)
""",
)
_test_roundtrip(
"""
variables: x, y, z
c1: [1.0 * x, y, z] in DualExponentialCone()
""",
"""
variables: x, y, z, a, b, c, d, e, f
minobjective: 1.0 * a + 1.0 * b + 1.0 * c + 1.0 * d + 1.0 * e + 1.0 * f
c1: [1.0 * x + 1.0 * a + -1.0 * b, y + 1.0 * c + -1.0 * d, z + 1.0 * e + -1.0 * f] in DualExponentialCone()
[a, b, c, d, e, f] in Nonnegatives(6)
""",
)
_test_roundtrip(
"""
variables: x, y, z
c1: [1.0 * x, y, z] in PowerCone(0.5)
""",
"""
variables: x, y, z, a, b, c, d, e, f
minobjective: 1.0 * a + 1.0 * b + 1.0 * c + 1.0 * d + 1.0 * e + 1.0 * f
c1: [1.0 * x + 1.0 * a + -1.0 * b, y + 1.0 * c + -1.0 * d, z + 1.0 * e + -1.0 * f] in PowerCone(0.5)
[a, b, c, d, e, f] in Nonnegatives(6)
""",
)
_test_roundtrip(
"""
variables: x, y, z
c1: [1.0 * x, y, z] in DualPowerCone(0.5)
""",
"""
variables: x, y, z, a, b, c, d, e, f
minobjective: 1.0 * a + 1.0 * b + 1.0 * c + 1.0 * d + 1.0 * e + 1.0 * f
c1: [1.0 * x + 1.0 * a + -1.0 * b, y + 1.0 * c + -1.0 * d, z + 1.0 * e + -1.0 * f] in DualPowerCone(0.5)
[a, b, c, d, e, f] in Nonnegatives(6)
""",
)
_test_roundtrip(
"""
variables: x, y, z
c1: [1.0 * x, y, z] in HyperRectangle([0.0, 0.0, 0.0], [1.0, 1.0, 1.0])
""",
"""
variables: x, y, z, a, b, c, d, e, f
minobjective: 1.0 * a + 1.0 * b + 1.0 * c + 1.0 * d + 1.0 * e + 1.0 * f
c1: [1.0 * x + 1.0 * a + -1.0 * b, y + 1.0 * c + -1.0 * d, z + 1.0 * e + -1.0 * f] in HyperRectangle([0.0, 0.0, 0.0], [1.0, 1.0, 1.0])
[a, b, c, d, e, f] in Nonnegatives(6)
""",
)
return
end

end # module

TestPenaltyRelaxation.runtests()
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