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[Utililties] fix dual objective value with open intervals #2823

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Aug 27, 2025
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[Utililties] fix dual objective value with open intervals #2823

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[Utililties] fix dual objective value with open intervals
odow Aug 27, 2025
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Add test
odow Aug 27, 2025
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42 changes: 24 additions & 18 deletions src/Utilities/results.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -88,6 +88,26 @@ function _dual_objective_value(
)
end

"""
Given lower <= f(x) <= upper [dual], return the expression to be multiplied by
the dual variable. This is one of the following cases:

1. f(x) - lower: if `lower > -Inf` and the lower bound is binding (either no
`upper` or `dual > 0`)
2. f(x) - upper: if `upper < Inf` and the upper bound is binding (either no
`lower` or `dual < 0`)
3. f(x): if `lower = -Inf` and `upper = Inf` or `dual = 0`
"""
function _constant_minus_bound(constant, lower, upper, dual)
if isfinite(lower) && (!isfinite(upper) || dual > zero(dual))
return constant - lower
elseif isfinite(upper) && (!isfinite(lower) || dual < zero(dual))
return constant - upper
else
return constant
end
end

function _dual_objective_value(
model::MOI.ModelLike,
ci::MOI.ConstraintIndex{<:MOI.AbstractScalarFunction,<:MOI.Interval},
Expand All @@ -97,14 +117,7 @@ function _dual_objective_value(
constant = MOI.constant(MOI.get(model, MOI.ConstraintFunction(), ci), T)
set = MOI.get(model, MOI.ConstraintSet(), ci)
dual = MOI.get(model, MOI.ConstraintDual(result_index), ci)
if dual < zero(dual)
# The dual is negative so it is in the dual of the MOI.LessThan cone
# hence the upper bound of the Interval set is tight
constant -= set.upper
else
# the lower bound is tight
constant -= set.lower
end
constant = _constant_minus_bound(constant, set.lower, set.upper, dual)
return set_dot(constant, dual, set)
end

Expand All @@ -118,17 +131,10 @@ function _dual_objective_value(
MOI.constant(MOI.get(model, MOI.ConstraintFunction(), ci), T)
set = MOI.get(model, MOI.ConstraintSet(), ci)
dual = MOI.get(model, MOI.ConstraintDual(result_index), ci)
constant = map(eachindex(func_constant)) do i
return func_constant[i] - if dual[i] < zero(dual[i])
# The dual is negative so it is in the dual of the MOI.LessThan cone
# hence the upper bound of the Interval set is tight
set.upper[i]
else
# the lower bound is tight
set.lower[i]
end
constants = map(enumerate(func_constant)) do (i, c)
return _constant_minus_bound(c, set.lower[i], set.upper[i], dual[i])
end
return set_dot(constant, dual, set)
return set_dot(constants, dual, set)
end

function _dual_objective_value(
Expand Down
98 changes: 98 additions & 0 deletions test/Utilities/results.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -51,6 +51,104 @@ function _test_hyperrectangle(T)
return
end

function test_dual_objective_value_open_interval_Interval()
inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
model = MOI.Utilities.MockOptimizer(inner)
# -Inf <= x[1] - 1.1 <= Inf
# -Inf <= x[2] - 1.2 <= 2.1
# -2.2 <= x[3] + 1.3 <= Inf
# -2.3 <= x[4] + 1.4 <= 2.4
x = MOI.add_variables(model, 4)
f = x .+ [-1.1, -1.2, 1.3, 1.4]
set = MOI.Interval.([-Inf, -Inf, -2.2, -2.3], [Inf, 2.1, Inf, 2.4])
c = MOI.add_constraint.(model, f, set)
for (dual, obj) in [
[0.0, 0.0, 0.0, 0.0] => 0.0,
# d[1]: -(-1.1) = 1.1
[-2.0, 0.0, 0.0, 0.0] => -2.2,
[-1.0, 0.0, 0.0, 0.0] => -1.1,
[1.0, 0.0, 0.0, 0.0] => 1.1,
[2.0, 0.0, 0.0, 0.0] => 2.2,
# d[2]: -(-1.2 - 2.1) = 3.3
[0.0, -2.0, 0.0, 0.0] => -6.6,
[0.0, -1.0, 0.0, 0.0] => -3.3,
[0.0, 1.0, 0.0, 0.0] => 3.3,
[0.0, 2.0, 0.0, 0.0] => 6.6,
# d[3]: -(1.3 - -2.2) = -3.5
[0.0, 0.0, -2.0, 0.0] => 7.0,
[0.0, 0.0, -1.0, 0.0] => 3.5,
[0.0, 0.0, 1.0, 0.0] => -3.5,
[0.0, 0.0, 2.0, 0.0] => -7.0,
# d[4]: -(1.4 - -2.3) = -3.7
# d[4]: -(1.4 - 2.4) = 1.0
[0.0, 0.0, 0.0, -2.0] => -2.0,
[0.0, 0.0, 0.0, -1.0] => -1.0,
[0.0, 0.0, 0.0, 1.0] => -3.7,
[0.0, 0.0, 0.0, 2.0] => -7.4,
#
[1.0, 1.0, 1.0, 1.0] => -2.8,
[-1.0, -1.0, -1.0, -1.0] => -1.9,
]
MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
MOI.set.(model, MOI.ConstraintDual(), c, dual)
d = MOI.Utilities.get_fallback(model, MOI.DualObjectiveValue(), Float64)
@test isapprox(d, obj)
MOI.set.(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
d = MOI.Utilities.get_fallback(model, MOI.DualObjectiveValue(), Float64)
@test isapprox(d, -obj)
end
return
end

function test_dual_objective_value_open_interval_Hyperrectangle()
inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
model = MOI.Utilities.MockOptimizer(inner)
# -Inf <= x[1] - 1.1 <= Inf
# -Inf <= x[2] - 1.2 <= 2.1
# -2.2 <= x[3] + 1.3 <= Inf
# -2.3 <= x[4] + 1.4 <= 2.4
x = MOI.add_variables(model, 4)
f = MOI.Utilities.vectorize(x .+ [-1.1, -1.2, 1.3, 1.4])
set = MOI.HyperRectangle([-Inf, -Inf, -2.2, -2.3], [Inf, 2.1, Inf, 2.4])
c = MOI.add_constraint(model, f, set)
for (dual, obj) in [
[0.0, 0.0, 0.0, 0.0] => 0.0,
# d[1]: -(-1.1) = 1.1
[-2.0, 0.0, 0.0, 0.0] => -2.2,
[-1.0, 0.0, 0.0, 0.0] => -1.1,
[1.0, 0.0, 0.0, 0.0] => 1.1,
[2.0, 0.0, 0.0, 0.0] => 2.2,
# d[2]: -(-1.2 - 2.1) = 3.3
[0.0, -2.0, 0.0, 0.0] => -6.6,
[0.0, -1.0, 0.0, 0.0] => -3.3,
[0.0, 1.0, 0.0, 0.0] => 3.3,
[0.0, 2.0, 0.0, 0.0] => 6.6,
# d[3]: -(1.3 - -2.2) = -3.5
[0.0, 0.0, -2.0, 0.0] => 7.0,
[0.0, 0.0, -1.0, 0.0] => 3.5,
[0.0, 0.0, 1.0, 0.0] => -3.5,
[0.0, 0.0, 2.0, 0.0] => -7.0,
# d[4]: -(1.4 - -2.3) = -3.7
# d[4]: -(1.4 - 2.4) = 1.0
[0.0, 0.0, 0.0, -2.0] => -2.0,
[0.0, 0.0, 0.0, -1.0] => -1.0,
[0.0, 0.0, 0.0, 1.0] => -3.7,
[0.0, 0.0, 0.0, 2.0] => -7.4,
#
[1.0, 1.0, 1.0, 1.0] => -2.8,
[-1.0, -1.0, -1.0, -1.0] => -1.9,
]
MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
MOI.set(model, MOI.ConstraintDual(), c, dual)
d = MOI.Utilities.get_fallback(model, MOI.DualObjectiveValue(), Float64)
@test isapprox(d, obj)
MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
d = MOI.Utilities.get_fallback(model, MOI.DualObjectiveValue(), Float64)
@test isapprox(d, -obj)
end
return
end

end # module TestResults

TestResults.runtests()
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