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Add bridge attribute for choosing the Cholesky backend #2985

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Add bridge attribute for choosing the Cholesky backend #2985

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131 changes: 111 additions & 20 deletions src/Bridges/Constraint/bridges/QuadtoSOCBridge.jl
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -4,6 +4,29 @@
# Use of this source code is governed by an MIT-style license that can be found
# in the LICENSE.md file or at https://opensource.org/licenses/MIT.

"""
QuadtoSOCSquareRoot <: MOI.AbstractConstraintAttribute

Constraint attribute to override the square root method used by
[`QuadtoSOCBridge`](@ref) for a specific quadratic constraint.

When set, this takes precedence over the default behavior of trying all
available methods. When not set, [`MOI.get`](@ref) returns `nothing`.

## Example

```julia
c = MOI.add_constraint(model, f, MOI.LessThan(1.0))
MOI.set(
model,
MOI.Bridges.Constraint.QuadtoSOCSquareRoot(),
c,
MOI.Bridges.Constraint._LinearAlgebra(),
)
```
"""
struct QuadtoSOCSquareRoot <: MOI.AbstractConstraintAttribute end

"""
QuadtoSOCBridge{T} <: Bridges.Constraint.AbstractBridge

Expand Down Expand Up @@ -46,15 +69,22 @@ Therefore, `QuadtoSOCBridge` implements the following reformulations:

This bridge errors if `Q` is not positive definite.
"""
struct QuadtoSOCBridge{T} <: AbstractBridge
soc::MOI.ConstraintIndex{
MOI.VectorAffineFunction{T},
MOI.RotatedSecondOrderCone,
mutable struct QuadtoSOCBridge{T} <: AbstractBridge
soc::Union{
Nothing,
MOI.ConstraintIndex{
MOI.VectorAffineFunction{T},
MOI.RotatedSecondOrderCone,
},
}
dimension::Int # dimension of the SOC constraint
less_than::Bool # whether the constraint was ≤ or ≥
set_constant::T # the constant that was on the set
index_to_variable_map::Vector{MOI.VariableIndex}
# Stored for final_touch
func::MOI.ScalarQuadraticFunction{T}
set::Union{MOI.LessThan{T},MOI.GreaterThan{T}}
method::Union{Nothing,_AbstractExt}
end

const QuadtoSOC{T,OT<:MOI.ModelLike} =
Expand Down Expand Up @@ -157,13 +187,63 @@ function bridge_constraint(
func::MOI.ScalarQuadraticFunction{T},
set::Union{MOI.LessThan{T},MOI.GreaterThan{T}},
) where {T}
# Delay reformulation until `final_touch` so that the
# `QuadtoSOCSquareRoot` attribute can override the method first.
less_than = set isa MOI.LessThan{T}
set_constant = MOI.constant(set)
MOI.throw_if_scalar_and_constant_not_zero(func, typeof(set))
return QuadtoSOCBridge{T}(
nothing,
0,
less_than,
set_constant,
MOI.VariableIndex[],
func,
set,
nothing,
)
end

MOI.supports(::MOI.ModelLike, ::QuadtoSOCSquareRoot, ::Type{<:QuadtoSOCBridge}) =
true

function MOI.set(
::MOI.ModelLike,
::QuadtoSOCSquareRoot,
bridge::QuadtoSOCBridge,
value::Union{Nothing,_AbstractExt},
)
bridge.method = value
return
end

function MOI.get(
::MOI.ModelLike,
::QuadtoSOCSquareRoot,
bridge::QuadtoSOCBridge,
)
return bridge.method
end

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

function MOI.Bridges.final_touch(
bridge::QuadtoSOCBridge{T},
model::MOI.ModelLike,
) where {T}
if bridge.soc !== nothing
return
end
func = bridge.func
set = bridge.set
less_than = bridge.less_than
scale = less_than ? -1 : 1
Q, index_to_variable_map =
_matrix_from_quadratic_terms(func.quadratic_terms)
if !less_than
LinearAlgebra.rmul!(Q, -1)
end
bridge.index_to_variable_map = index_to_variable_map
# Construct the VectorAffineFunction. We're aiming for:
# | 1 |
# | -a^T x + ub | ∈ RotatedSecondOrderCone()
Expand All @@ -175,10 +255,15 @@ function bridge_constraint(
MOI.ScalarAffineTerm(scale * term.coefficient, term.variable),
) for term in func.affine_terms
]
sqrt_ret = _compute_sparse_sqrt(LinearAlgebra.Symmetric(Q))
Q_sym = LinearAlgebra.Symmetric(Q)
sqrt_ret = if bridge.method !== nothing
_compute_sparse_sqrt(bridge.method, Q_sym)
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@odow odow Apr 1, 2026

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For example, adding this attribute would also require us to make these methods public and commit to their API, etc.

else
_compute_sparse_sqrt(Q_sym)
end
if sqrt_ret === nothing
msg = _get_sqrt_error_message(is_defined(_CliqueTrees()))
return throw(MOI.UnsupportedConstraint{typeof(func),typeof(set)}(msg))
throw(MOI.UnsupportedConstraint{typeof(func),typeof(set)}(msg))
end
for (i, j, v) in zip(sqrt_ret[1], sqrt_ret[2], sqrt_ret[3])
push!(
Expand All @@ -190,19 +275,13 @@ function bridge_constraint(
)
end
# This is the [1, ub, 0] vector...
set_constant = MOI.constant(set)
MOI.throw_if_scalar_and_constant_not_zero(func, typeof(set))
set_constant = bridge.set_constant
vector_constant = vcat(one(T), -scale * set_constant, zeros(T, size(Q, 1)))
f = MOI.VectorAffineFunction(vector_terms, vector_constant)
dimension = MOI.output_dimension(f)
soc = MOI.add_constraint(model, f, MOI.RotatedSecondOrderCone(dimension))
return QuadtoSOCBridge(
soc,
dimension,
less_than,
set_constant,
index_to_variable_map,
)
bridge.dimension = MOI.output_dimension(f)
bridge.soc =
MOI.add_constraint(model, f, MOI.RotatedSecondOrderCone(bridge.dimension))
return
end

function _matrix_from_quadratic_terms(
Expand Down Expand Up @@ -267,13 +346,13 @@ end

# Attributes, Bridge acting as a model
function MOI.get(
::QuadtoSOCBridge{T},
bridge::QuadtoSOCBridge{T},
::MOI.NumberOfConstraints{
MOI.VectorAffineFunction{T},
MOI.RotatedSecondOrderCone,
},
)::Int64 where {T}
return 1
return bridge.soc === nothing ? 0 : 1
end

function MOI.get(
Expand All @@ -283,12 +362,21 @@ function MOI.get(
MOI.RotatedSecondOrderCone,
},
) where {T}
if bridge.soc === nothing
return MOI.ConstraintIndex{
MOI.VectorAffineFunction{T},
MOI.RotatedSecondOrderCone,
}[]
end
return [bridge.soc]
end

# References
function MOI.delete(model::MOI.ModelLike, bridge::QuadtoSOCBridge)
MOI.delete(model, bridge.soc)
if bridge.soc !== nothing
MOI.delete(model, bridge.soc)
bridge.soc = nothing
end
return
end

Expand Down Expand Up @@ -485,6 +573,9 @@ function MOI.get(
attr::MOI.ConstraintFunction,
b::QuadtoSOCBridge{T},
) where {T}
if b.soc === nothing
return copy(b.func)
end
f = MOI.get(model, attr, b.soc)
fs = MOI.Utilities.eachscalar(f)
q = zero(MOI.ScalarQuadraticFunction{T})
Expand Down
77 changes: 75 additions & 2 deletions test/Bridges/Constraint/test_QuadtoSOCBridge.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -31,13 +31,19 @@ function test_error_for_nonconvex_quadratic_constraints()
model = MOI.Bridges.Constraint.QuadtoSOC{Float64}(inner)
x = MOI.add_variable(model)
F = MOI.ScalarQuadraticFunction{Float64}
# Error is now thrown at final_touch, not add_constraint
MOI.add_constraint(model, 1.0 * x * x, MOI.GreaterThan(0.0))
@test_throws(
MOI.UnsupportedConstraint{F,MOI.GreaterThan{Float64}},
MOI.add_constraint(model, 1.0 * x * x, MOI.GreaterThan(0.0))
MOI.Bridges.final_touch(model),
)
MOI.empty!(model)
MOI.add_variable(model)
x = MOI.get(model, MOI.ListOfVariableIndices())[1]
MOI.add_constraint(model, -1.0 * x * x, MOI.LessThan(0.0))
@test_throws(
MOI.UnsupportedConstraint{F,MOI.LessThan{Float64}},
MOI.add_constraint(model, -1.0 * x * x, MOI.LessThan(0.0))
MOI.Bridges.final_touch(model),
)
return
end
Expand Down Expand Up @@ -65,6 +71,7 @@ function test_quadratic_constraints_with_2_variables()
),
)
MOI.Test.test_constraint_qcp_duplicate_off_diagonal(bridged_mock, config)
MOI.Bridges.final_touch(bridged_mock)
ci = first(
MOI.get(
mock,
Expand Down Expand Up @@ -164,6 +171,7 @@ function test_fill_reducing_permutation()
Q = Float64[2 1 1; 1 2 0; 1 0 2]
f = 0.5 * x' * Q * x
MOI.add_constraint(bridge, f, MOI.LessThan(2.0))
MOI.Bridges.final_touch(bridge)
indices = MOI.get(
model,
MOI.ListOfConstraintIndices{
Expand Down Expand Up @@ -331,6 +339,7 @@ function test_semidefinite_cholesky_fail()
x = MOI.add_variables(model, 2)
f = 0.5 * x[1] * x[1] + 1.0 * x[1] * x[2] + 0.5 * x[2] * x[2]
c = MOI.add_constraint(model, f, MOI.LessThan(1.0))
MOI.Bridges.final_touch(model)
F, S = MOI.VectorAffineFunction{Float64}, MOI.RotatedSecondOrderCone
ci = only(MOI.get(inner, MOI.ListOfConstraintIndices{F,S}()))
g = MOI.get(inner, MOI.ConstraintFunction(), ci)
Expand Down Expand Up @@ -435,6 +444,7 @@ function test_clique_trees_semidefinite_cholesky_fail()
x = MOI.add_variables(model, 2)
f = 0.5 * x[1] * x[1] + 1.0 * x[1] * x[2] + 0.5 * x[2] * x[2]
c = MOI.add_constraint(model, f, MOI.LessThan(1.0))
MOI.Bridges.final_touch(model)
F, S = MOI.VectorAffineFunction{Float64}, MOI.RotatedSecondOrderCone
ci = only(MOI.get(inner, MOI.ListOfConstraintIndices{F,S}()))
g = MOI.get(inner, MOI.ConstraintFunction(), ci)
Expand All @@ -454,6 +464,7 @@ function test_clique_trees_early_zero_pivot()
# Q = [1 1 0; 1 1 0; 0 0 1]
f = sum(0.5 * x[i] * x[i] for i in 1:3) + 1.0 * x[1] * x[2]
c = MOI.add_constraint(model, f, MOI.LessThan(1.0))
MOI.Bridges.final_touch(model)
F, S = MOI.VectorAffineFunction{Float64}, MOI.RotatedSecondOrderCone
ci = only(MOI.get(inner, MOI.ListOfConstraintIndices{F,S}()))
g = MOI.get(inner, MOI.ConstraintFunction(), ci)
Expand Down Expand Up @@ -482,6 +493,68 @@ function test_is_defined_default_fallback()
return
end

function test_quad_to_soc_square_root_attribute()
inner = MOI.Utilities.Model{Float64}()
model = MOI.Bridges.Constraint.QuadtoSOC{Float64}(inner)
x = MOI.add_variables(model, 2)
f = 1.0 * x[1] * x[1] + 1.0 * x[2] * x[2]
c = MOI.add_constraint(model, f, MOI.LessThan(1.0))
attr = MOI.Bridges.Constraint.QuadtoSOCSquareRoot()
F = MOI.ScalarQuadraticFunction{Float64}
S = MOI.LessThan{Float64}
@test MOI.supports(model, attr, MOI.ConstraintIndex{F,S})
# Default is nothing
@test MOI.get(model, attr, c) === nothing
# Set to _LinearAlgebra
la = MOI.Bridges.Constraint._LinearAlgebra()
MOI.set(model, attr, c, la)
@test MOI.get(model, attr, c) === la
# final_touch uses the specified method
MOI.Bridges.final_touch(model)
F2, S2 = MOI.VectorAffineFunction{Float64}, MOI.RotatedSecondOrderCone
ci = only(MOI.get(inner, MOI.ListOfConstraintIndices{F2,S2}()))
g = MOI.get(inner, MOI.ConstraintFunction(), ci)
@test MOI.output_dimension(g) == 4 # [1, rhs, Ux...]
return
end

function test_quad_to_soc_square_root_attribute_clique_trees()
inner = MOI.Utilities.Model{Float64}()
model = MOI.Bridges.Constraint.QuadtoSOC{Float64}(inner)
x = MOI.add_variables(model, 2)
f = 1.0 * x[1] * x[1] + 1.0 * x[2] * x[2]
c = MOI.add_constraint(model, f, MOI.LessThan(1.0))
attr = MOI.Bridges.Constraint.QuadtoSOCSquareRoot()
ct = MOI.Bridges.Constraint._CliqueTrees()
MOI.set(model, attr, c, ct)
@test MOI.get(model, attr, c) === ct
MOI.Bridges.final_touch(model)
F, S = MOI.VectorAffineFunction{Float64}, MOI.RotatedSecondOrderCone
ci = only(MOI.get(inner, MOI.ListOfConstraintIndices{F,S}()))
g = MOI.get(inner, MOI.ConstraintFunction(), ci)
@test MOI.output_dimension(g) == 4
return
end

function test_quad_to_soc_square_root_attribute_reset()
inner = MOI.Utilities.Model{Float64}()
model = MOI.Bridges.Constraint.QuadtoSOC{Float64}(inner)
x = MOI.add_variables(model, 2)
f = 1.0 * x[1] * x[1] + 1.0 * x[2] * x[2]
c = MOI.add_constraint(model, f, MOI.LessThan(1.0))
attr = MOI.Bridges.Constraint.QuadtoSOCSquareRoot()
la = MOI.Bridges.Constraint._LinearAlgebra()
MOI.set(model, attr, c, la)
# Reset to nothing (default behavior)
MOI.set(model, attr, c, nothing)
@test MOI.get(model, attr, c) === nothing
MOI.Bridges.final_touch(model)
F, S = MOI.VectorAffineFunction{Float64}, MOI.RotatedSecondOrderCone
ci = only(MOI.get(inner, MOI.ListOfConstraintIndices{F,S}()))
@test ci isa MOI.ConstraintIndex
return
end

end # module

TestConstraintQuadToSOC.runtests()
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