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[Utilities] simplify _dual_objective_value #2826

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[Utilities] simplify _dual_objective_value
odow Aug 28, 2025
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172 changes: 66 additions & 106 deletions src/Utilities/results.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -52,112 +52,6 @@ end

# MOI.DualObjectiveValue

function _constraint_constant(
model::MOI.ModelLike,
ci::MOI.ConstraintIndex{
<:MOI.AbstractVectorFunction,
<:MOI.AbstractVectorSet,
},
::Type{T},
) where {T}
return MOI.constant(MOI.get(model, MOI.ConstraintFunction(), ci), T)
end

function _constraint_constant(
model::MOI.ModelLike,
ci::MOI.ConstraintIndex{
<:MOI.AbstractScalarFunction,
<:MOI.AbstractScalarSet,
},
::Type{T},
) where {T}
return MOI.constant(MOI.get(model, MOI.ConstraintFunction(), ci), T) -
MOI.constant(MOI.get(model, MOI.ConstraintSet(), ci))
end

function _dual_objective_value(
model::MOI.ModelLike,
ci::MOI.ConstraintIndex,
::Type{T},
result_index::Integer,
) where {T}
return set_dot(
_constraint_constant(model, ci, T),
MOI.get(model, MOI.ConstraintDual(result_index), ci),
MOI.get(model, MOI.ConstraintSet(), ci),
)
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},
::Type{T},
result_index::Integer,
) where {T}
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)
constant = _constant_minus_bound(constant, set.lower, set.upper, dual)
return set_dot(constant, dual, set)
end

function _dual_objective_value(
model::MOI.ModelLike,
ci::MOI.ConstraintIndex{<:MOI.AbstractVectorFunction,<:MOI.HyperRectangle},
::Type{T},
result_index::Integer,
) where {T}
func_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)
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(constants, dual, set)
end

function _dual_objective_value(
model::MOI.ModelLike,
::Type{F},
::Type{S},
::Type{T},
result_index::Integer,
) where {T,F<:MOI.AbstractFunction,S<:MOI.AbstractSet}
value = zero(T)
if F == variable_function_type(S) && !_has_constant(S)
return value # Shortcut
end
for ci in MOI.get(model, MOI.ListOfConstraintIndices{F,S}())
value += _dual_objective_value(model, ci, T, result_index)
end
return value
end

_has_constant(::Type{<:MOI.AbstractScalarSet}) = true
_has_constant(::Type{<:MOI.AbstractVectorSet}) = false
_has_constant(::Type{<:MOI.HyperRectangle}) = true

"""
get_fallback(
model::MOI.ModelLike,
Expand Down Expand Up @@ -192,6 +86,72 @@ function get_fallback(
return value::T
end

function _dual_objective_value(
model::MOI.ModelLike,
::Type{F},
::Type{S},
::Type{T},
result_index::Integer,
)::T where {T,F<:MOI.AbstractFunction,S<:MOI.AbstractSet}
value = zero(T)
if F == variable_function_type(S) && !_variable_set_in_dual_objective(S)
# Early return. This is a constraint like x in R_+, so no contribution
# appears in the dual objective.
return value
end
for ci in MOI.get(model, MOI.ListOfConstraintIndices{F,S}())
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)
value += _dual_objective_dot(constant, dual, set)
end
return value
end

_variable_set_in_dual_objective(::Type{<:MOI.AbstractSet}) = false

_variable_set_in_dual_objective(::Type{<:MOI.EqualTo}) = true

_variable_set_in_dual_objective(::Type{<:MOI.GreaterThan}) = true

_variable_set_in_dual_objective(::Type{<:MOI.LessThan}) = true

_variable_set_in_dual_objective(::Type{<:MOI.Interval}) = true

_variable_set_in_dual_objective(::Type{<:MOI.HyperRectangle}) = true

_dual_objective_dot(x, y, set) = set_dot(x, y, set)

_dual_objective_dot(x, y, set::MOI.EqualTo) = (x - set.value) * y

_dual_objective_dot(x, y, set::MOI.LessThan) = (x - set.upper) * y

_dual_objective_dot(x, y, set::MOI.GreaterThan) = (x - set.lower) * y

function _dual_objective_dot(x, y, set::MOI.Interval)
if isfinite(set.lower) && (!isfinite(set.upper) || y > zero(y))
return (x - set.lower) * y
elseif isfinite(set.upper) && (!isfinite(set.lower) || y < zero(y))
return (x - set.upper) * y
end
return x * y
end

function _dual_objective_dot(x, y, set::MOI.HyperRectangle)
@assert length(x) == length(y) == MOI.dimension(set)
ret = zero(eltype(x))
for (xi, yi, li, ui) in zip(x, y, set.lower, set.upper)
if isfinite(li) && (!isfinite(ui) || yi > zero(yi))
ret += (xi - li) * yi
elseif isfinite(ui) && (!isfinite(li) || yi < zero(yi))
ret += (xi - ui) * yi
else
ret += xi * yi
end
end
return ret
end

# MOI.ConstraintPrimal

"""
Expand Down
2 changes: 1 addition & 1 deletion test/Bridges/Constraint/NormSpectralBridge.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -197,7 +197,7 @@ function test_NormNuclear()
mock,
var_primal,
(MOI.ScalarAffineFunction{Float64}, MOI.GreaterThan{Float64}) =>
[[1.0]],
[1.0],
(
MOI.VectorAffineFunction{Float64},
MOI.PositiveSemidefiniteConeTriangle,
Expand Down
104 changes: 103 additions & 1 deletion test/Utilities/results.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -51,6 +51,57 @@ function _test_hyperrectangle(T)
return
end

function test_dual_objective_value_open_interval_Interval_variable_index()
inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
model = MOI.Utilities.MockOptimizer(
inner;
eval_variable_constraint_dual = false,
)
# -Inf <= x[1] <= Inf
# -Inf <= x[2] <= 2.1
# -2.2 <= x[3] <= Inf
# -2.3 <= x[4] <= 2.4
x = MOI.add_variables(model, 4)
set = MOI.Interval.([-Inf, -Inf, -2.2, -2.3], [Inf, 2.1, Inf, 2.4])
c = MOI.add_constraint.(model, x, set)
for (dual, obj) in [
[0.0, 0.0, 0.0, 0.0] => 0.0,
# d[1]
[-2.0, 0.0, 0.0, 0.0] => 0.0,
[-1.0, 0.0, 0.0, 0.0] => 0.0,
[1.0, 0.0, 0.0, 0.0] => 0.0,
[2.0, 0.0, 0.0, 0.0] => 0.0,
# d[2]: -(-2.1) = 2.1
[0.0, -2.0, 0.0, 0.0] => -4.2,
[0.0, -1.0, 0.0, 0.0] => -2.1,
[0.0, 1.0, 0.0, 0.0] => 2.1,
[0.0, 2.0, 0.0, 0.0] => 4.2,
# d[3]: -(- -2.2) = -2.2
[0.0, 0.0, -2.0, 0.0] => 4.4,
[0.0, 0.0, -1.0, 0.0] => 2.2,
[0.0, 0.0, 1.0, 0.0] => -2.2,
[0.0, 0.0, 2.0, 0.0] => -4.4,
# d[4]: -(- -2.3) = -2.3
# d[4]: -(- 2.4) = 2.4
[0.0, 0.0, 0.0, -2.0] => -4.8,
[0.0, 0.0, 0.0, -1.0] => -2.4,
[0.0, 0.0, 0.0, 1.0] => -2.3,
[0.0, 0.0, 0.0, 2.0] => -4.6,
#
[1.0, 1.0, 1.0, 1.0] => -2.4,
[-1.0, -1.0, -1.0, -1.0] => -2.3,
]
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_Interval()
inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
model = MOI.Utilities.MockOptimizer(inner)
Expand Down Expand Up @@ -93,7 +144,58 @@ function test_dual_objective_value_open_interval_Interval()
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)
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_variable_index()
inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
model = MOI.Utilities.MockOptimizer(
inner;
eval_variable_constraint_dual = false,
)
# -Inf <= x[1] <= Inf
# -Inf <= x[2] <= 2.1
# -2.2 <= x[3] <= Inf
# -2.3 <= x[4] <= 2.4
x = MOI.add_variables(model, 4)
set = MOI.HyperRectangle([-Inf, -Inf, -2.2, -2.3], [Inf, 2.1, Inf, 2.4])
c = MOI.add_constraint(model, MOI.VectorOfVariables(x), set)
for (dual, obj) in [
[0.0, 0.0, 0.0, 0.0] => 0.0,
# d[1]
[-2.0, 0.0, 0.0, 0.0] => 0.0,
[-1.0, 0.0, 0.0, 0.0] => 0.0,
[1.0, 0.0, 0.0, 0.0] => 0.0,
[2.0, 0.0, 0.0, 0.0] => 0.0,
# d[2]: -(-2.1) = 2.1
[0.0, -2.0, 0.0, 0.0] => -4.2,
[0.0, -1.0, 0.0, 0.0] => -2.1,
[0.0, 1.0, 0.0, 0.0] => 2.1,
[0.0, 2.0, 0.0, 0.0] => 4.2,
# d[3]: -(- -2.2) = -2.2
[0.0, 0.0, -2.0, 0.0] => 4.4,
[0.0, 0.0, -1.0, 0.0] => 2.2,
[0.0, 0.0, 1.0, 0.0] => -2.2,
[0.0, 0.0, 2.0, 0.0] => -4.4,
# d[4]: -(- -2.3) = -2.3
# d[4]: -(- 2.4) = 2.4
[0.0, 0.0, 0.0, -2.0] => -4.8,
[0.0, 0.0, 0.0, -1.0] => -2.4,
[0.0, 0.0, 0.0, 1.0] => -2.3,
[0.0, 0.0, 0.0, 2.0] => -4.6,
#
[1.0, 1.0, 1.0, 1.0] => -2.4,
[-1.0, -1.0, -1.0, -1.0] => -2.3,
]
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
Expand Down
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