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Merged
blegat merged 4 commits into from
Jul 7, 2026
Merged

Preserve bounds in SplitIntervalBridge #71

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6e19e76
Preserve bounds in SplitIntervalBridge
blegat Jul 6, 2026
f523c8e
Simplify
blegat Jul 6, 2026
d9c9656
Fix format
blegat Jul 6, 2026
208d3bf
Add tests
blegat Jul 7, 2026
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94 changes: 87 additions & 7 deletions src/Bridges/SplitIntervalBridge.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -19,6 +19,22 @@ The input function can be any `MOI.AbstractVectorFunction` (the first
component `x` may be affine or quadratic); only the second component `y`
must be a variable.

Since the lower bound of `y` is strictly smaller than its upper bound,
`xp` and `xn` cannot both be nonzero at a feasible point, so
`xp = max(x, 0)` and `xn = min(x, 0)`. In
[`MOI.Bridges.final_touch`](@ref), if the activity `x` has finite lower
and upper bounds `[lb, ub]`, the bounds `xp <= max(ub, 0)` and
`xn >= min(lb, 0)` are added. This is done in
[`MOI.Bridges.final_touch`](@ref) and not in
`MOI.Bridges.Constraint.bridge_constraint` because the bounds of `x` may
be set after the constraint is bridged. These bounds are needed by
[`MOI.Bridges.Constraint.SOS1ToMILPBridge`](@ref) in case the inner solver
does not support [`MOI.SOS1`](@ref) constraints. Since that bridge
requires both bounds anyway (`xp` and `xn` each appear in an
[`MOI.SOS1`](@ref) constraint), we use the same
`MOI.Utilities.get_bounds` method and add nothing when either bound is
infinite.

## Source node

`SplitIntervalBridge` supports:
Expand All @@ -35,11 +51,15 @@ must be a variable.
* [`MOI.VectorOfVariables`](@ref) in
[`ComplementsWithSetType{MOI.LessThan{T}}`](@ref)
* `G` in [`MOI.EqualTo{T}`](@ref) (the splitting equality)
* [`MOI.VariableIndex`](@ref) in [`MOI.LessThan{T}`](@ref) and
[`MOI.VariableIndex`](@ref) in [`MOI.GreaterThan{T}`](@ref)
(the bounds on `xp` and `xn`, added in
[`MOI.Bridges.final_touch`](@ref) if the activity is bounded)

where `G` is the scalar function type of the first component.

"""
struct SplitIntervalBridge{
mutable struct SplitIntervalBridge{
T,
G<:MOI.AbstractScalarFunction,
F<:MOI.AbstractVectorFunction,
Expand All @@ -57,6 +77,14 @@ struct SplitIntervalBridge{
xn::MOI.VariableIndex
func::F
set::ComplementsWithSetType{MOI.Interval{T}}
xp_upper::Union{
Nothing,
MOI.ConstraintIndex{MOI.VariableIndex,MOI.LessThan{T}},
}
xn_lower::Union{
Nothing,
MOI.ConstraintIndex{MOI.VariableIndex,MOI.GreaterThan{T}},
}
end

function MOI.Bridges.Constraint.bridge_constraint(
Expand Down Expand Up @@ -110,6 +138,8 @@ function MOI.Bridges.Constraint.bridge_constraint(
xn,
func,
set,
nothing,
nothing,
)
end

Expand Down Expand Up @@ -151,6 +181,46 @@ function MOI.set(
return
end

MOI.Bridges.needs_final_touch(::SplitIntervalBridge) = true

function MOI.Bridges.final_touch(
bridge::SplitIntervalBridge{T},
model::MOI.ModelLike,
) where {T}
x = first(MOI.Utilities.eachscalar(bridge.func))
ret = if x isa MOI.VariableIndex || x isa MOI.ScalarAffineFunction{T}
cache = Dict{MOI.VariableIndex,NTuple{2,T}}()
MOI.Utilities.get_bounds(model, cache, x)

@blegat blegat Jul 6, 2026

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@odow What's weird here is that get_bound returns nothing even if one of the two bounds exists. It makes sense for SOS1ToMILP since you want two bounds but in here, if there is only one bound, we could already work with it

else
nothing
end
if ret === nothing
if bridge.xp_upper !== nothing
MOI.delete(model, bridge.xp_upper)
bridge.xp_upper = nothing
end
if bridge.xn_lower !== nothing
MOI.delete(model, bridge.xn_lower)
bridge.xn_lower = nothing
end
return
end
lb, ub = ret
upper = MOI.LessThan(max(ub, zero(T)))
if bridge.xp_upper === nothing
bridge.xp_upper = MOI.add_constraint(model, bridge.xp, upper)
elseif MOI.get(model, MOI.ConstraintSet(), bridge.xp_upper) != upper
MOI.set(model, MOI.ConstraintSet(), bridge.xp_upper, upper)
end
lower = MOI.GreaterThan(min(lb, zero(T)))
if bridge.xn_lower === nothing
bridge.xn_lower = MOI.add_constraint(model, bridge.xn, lower)
elseif MOI.get(model, MOI.ConstraintSet(), bridge.xn_lower) != lower
MOI.set(model, MOI.ConstraintSet(), bridge.xn_lower, lower)
end
return
end

# Bridge metadata

function MOI.Bridges.added_constrained_variable_types(
Expand All @@ -166,6 +236,8 @@ function MOI.Bridges.added_constraint_types(
(MOI.VectorOfVariables, ComplementsWithSetType{MOI.GreaterThan{T}}),
(MOI.VectorOfVariables, ComplementsWithSetType{MOI.LessThan{T}}),
(G, MOI.EqualTo{T}),
(MOI.VariableIndex, MOI.GreaterThan{T}),
(MOI.VariableIndex, MOI.LessThan{T}),
]
end

Expand All @@ -181,37 +253,45 @@ end
# constraints that must be reported as part of the bridge.

function MOI.get(
::SplitIntervalBridge{T},
bridge::SplitIntervalBridge{T},
::MOI.NumberOfConstraints{MOI.VariableIndex,MOI.GreaterThan{T}},
)::Int64 where {T}
return 1
return 1 + (bridge.xn_lower !== nothing)
end

function MOI.get(
bridge::SplitIntervalBridge{T},
::MOI.ListOfConstraintIndices{MOI.VariableIndex,MOI.GreaterThan{T}},
) where {T}
return [
ret = [
MOI.ConstraintIndex{MOI.VariableIndex,MOI.GreaterThan{T}}(
bridge.xp.value,
),
]
if bridge.xn_lower !== nothing
push!(ret, bridge.xn_lower)
end
return ret
end

function MOI.get(
::SplitIntervalBridge{T},
bridge::SplitIntervalBridge{T},
::MOI.NumberOfConstraints{MOI.VariableIndex,MOI.LessThan{T}},
)::Int64 where {T}
return 1
return 1 + (bridge.xp_upper !== nothing)
end

function MOI.get(
bridge::SplitIntervalBridge{T},
::MOI.ListOfConstraintIndices{MOI.VariableIndex,MOI.LessThan{T}},
) where {T}
return [
ret = [
MOI.ConstraintIndex{MOI.VariableIndex,MOI.LessThan{T}}(bridge.xn.value),
]
if bridge.xp_upper !== nothing
push!(ret, bridge.xp_upper)
end
return ret
end

function MOI.get(
Expand Down
188 changes: 188 additions & 0 deletions test/Bridges/test_SplitIntervalBridge.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -64,6 +64,194 @@ function test_VectorAffineFunction_input()
return
end

function test_bounded_activity()
MOI.Bridges.runtests(
MathOptComplements.Bridges.SplitIntervalBridge,
"""
variables: x, y
x in Interval(-2.0, 4.0)
y in Interval(0.0, 1.0)
[x, y] in $M.ComplementsWithSetType{MOI.Interval{Float64}}(2)
""",
"""
variables: x, y, xp, xn
x in Interval(-2.0, 4.0)
y in Interval(0.0, 1.0)
xp >= 0.0
xp <= 4.0
xn <= 0.0
xn >= -2.0
1.0 * x + -1.0 * xp + -1.0 * xn == 0.0
[xp, y] in $M.ComplementsWithSetType{MOI.GreaterThan{Float64}}(2)
[xn, y] in $M.ComplementsWithSetType{MOI.LessThan{Float64}}(2)
""";
cannot_unbridge = true,
)
return
end

# The bounds on `xp` and `xn` are only needed by `SOS1ToMILPBridge`, which
# requires both bounds of the activity anyway, so no bound is added when
# the activity is bounded on only one side.
function test_upper_bounded_activity()
MOI.Bridges.runtests(
MathOptComplements.Bridges.SplitIntervalBridge,
"""
variables: x, y
x <= 4.0
y in Interval(0.0, 1.0)
[x, y] in $M.ComplementsWithSetType{MOI.Interval{Float64}}(2)
""",
"""
variables: x, y, xp, xn
x <= 4.0
y in Interval(0.0, 1.0)
xp >= 0.0
xn <= 0.0
1.0 * x + -1.0 * xp + -1.0 * xn == 0.0
[xp, y] in $M.ComplementsWithSetType{MOI.GreaterThan{Float64}}(2)
[xn, y] in $M.ComplementsWithSetType{MOI.LessThan{Float64}}(2)
""";
cannot_unbridge = true,
)
return
end

function test_lower_bounded_activity()
MOI.Bridges.runtests(
MathOptComplements.Bridges.SplitIntervalBridge,
"""
variables: x, y
x >= -2.0
y in Interval(0.0, 1.0)
[x, y] in $M.ComplementsWithSetType{MOI.Interval{Float64}}(2)
""",
"""
variables: x, y, xp, xn
x >= -2.0
y in Interval(0.0, 1.0)
xp >= 0.0
xn <= 0.0
1.0 * x + -1.0 * xp + -1.0 * xn == 0.0
[xp, y] in $M.ComplementsWithSetType{MOI.GreaterThan{Float64}}(2)
[xn, y] in $M.ComplementsWithSetType{MOI.LessThan{Float64}}(2)
""";
cannot_unbridge = true,
)
return
end

function test_positive_activity()
# With `x ∈ [1, 4]`, the negative part `xn = min(x, 0)` is fixed to zero.
MOI.Bridges.runtests(
MathOptComplements.Bridges.SplitIntervalBridge,
"""
variables: x, y
x in Interval(1.0, 4.0)
y in Interval(0.0, 1.0)
[x, y] in $M.ComplementsWithSetType{MOI.Interval{Float64}}(2)
""",
"""
variables: x, y, xp, xn
x in Interval(1.0, 4.0)
y in Interval(0.0, 1.0)
xp >= 0.0
xp <= 4.0
xn <= 0.0
xn >= 0.0
1.0 * x + -1.0 * xp + -1.0 * xn == 0.0
[xp, y] in $M.ComplementsWithSetType{MOI.GreaterThan{Float64}}(2)
[xn, y] in $M.ComplementsWithSetType{MOI.LessThan{Float64}}(2)
""";
cannot_unbridge = true,
)
return
end

function test_bounded_affine_activity()
# The activity `2x + 1` with `x ∈ [-2, 4]` lies in `[-3, 9]`.
MOI.Bridges.runtests(
MathOptComplements.Bridges.SplitIntervalBridge,
"""
variables: x, y
x in Interval(-2.0, 4.0)
y in Interval(0.0, 1.0)
[2.0 * x + 1.0, y] in $M.ComplementsWithSetType{MOI.Interval{Float64}}(2)
""",
"""
variables: x, y, xp, xn
x in Interval(-2.0, 4.0)
y in Interval(0.0, 1.0)
xp >= 0.0
xp <= 9.0
xn <= 0.0
xn >= -3.0
2.0 * x + -1.0 * xp + -1.0 * xn == -1.0
[xp, y] in $M.ComplementsWithSetType{MOI.GreaterThan{Float64}}(2)
[xn, y] in $M.ComplementsWithSetType{MOI.LessThan{Float64}}(2)
""";
cannot_unbridge = true,
)
return
end

function test_final_touch_bound_modification()
T = Float64
inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{T}())
model = MOI.Bridges.Constraint.SingleBridgeOptimizer{
MathOptComplements.Bridges.SplitIntervalBridge{T},
}(
inner,
)
x = MOI.add_variable(model)
y, _ = MOI.add_constrained_variable(model, MOI.Interval(zero(T), one(T)))
MOI.add_constraint(
model,
MOI.VectorOfVariables([x, y]),
MathOptComplements.ComplementsWithSetType{MOI.Interval{T}}(2),
)
F = MOI.VariableIndex
upper_sets(m) = [
MOI.get(m, MOI.ConstraintSet(), ci) for
ci in MOI.get(m, MOI.ListOfConstraintIndices{F,MOI.LessThan{T}}())
]
lower_sets(m) = [
MOI.get(m, MOI.ConstraintSet(), ci) for ci in
MOI.get(m, MOI.ListOfConstraintIndices{F,MOI.GreaterThan{T}}())
]
# `x` only has a lower bound so no bound is added on `xp` nor `xn`:
# the only `LessThan` is `xn <= 0` and the `GreaterThan` are `x >= -1`
# and `xp >= 0`
MOI.add_constraint(model, x, MOI.GreaterThan(T(-1)))
MOI.Bridges.final_touch(model)
@test upper_sets(inner) == [MOI.LessThan(zero(T))]
@test sort(lower_sets(inner); by = s -> s.lower) ==
[MOI.GreaterThan(T(-1)), MOI.GreaterThan(zero(T))]
# Adding `x <= 4` adds `xp <= 4` and `xn >= -1` at the next final_touch
c_ub = MOI.add_constraint(model, x, MOI.LessThan(T(4)))
MOI.Bridges.final_touch(model)
@test sort(upper_sets(inner); by = s -> s.upper) ==
[MOI.LessThan(zero(T)), MOI.LessThan(T(4)), MOI.LessThan(T(4))]
@test sort(lower_sets(inner); by = s -> s.lower) == [
MOI.GreaterThan(T(-1)),
MOI.GreaterThan(T(-1)),
MOI.GreaterThan(zero(T)),
]
# Tightening to `x <= 2` updates the bound of `xp`
MOI.set(model, MOI.ConstraintSet(), c_ub, MOI.LessThan(T(2)))
MOI.Bridges.final_touch(model)
@test sort(upper_sets(inner); by = s -> s.upper) ==
[MOI.LessThan(zero(T)), MOI.LessThan(T(2)), MOI.LessThan(T(2))]
# Removing the upper bound of `x` removes the bounds of both `xp`
# and `xn`
MOI.delete(model, c_ub)
MOI.Bridges.final_touch(model)
@test upper_sets(inner) == [MOI.LessThan(zero(T))]
@test sort(lower_sets(inner); by = s -> s.lower) ==
[MOI.GreaterThan(T(-1)), MOI.GreaterThan(zero(T))]
return
end

end # TestSplitIntervalBridge

TestSplitIntervalBridge.runtests()
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