[Bridges.Constraint] add bridges in alphabetical order

src/Bridges/Constraint/Constraint.jl

@@ -29,84 +29,113 @@ Add all bridges defined in the `Bridges.Constraint` submodule to `model`.
 The coefficient type used is `T`.
 """
 function add_all_bridges(model, ::Type{T}) where {T}
-    if T <: AbstractFloat
+    MOI.Bridges.add_bridge(model, AllDifferentToCountDistinctBridge{T})
+    MOI.Bridges.add_bridge(model, BinPackingToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, CircuitToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, ComplexNormInfinityToSecondOrderConeBridge{T})
+    MOI.Bridges.add_bridge(model, CountAtLeastToCountBelongsBridge{T})
+    MOI.Bridges.add_bridge(model, CountBelongsToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, CountDistinctToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, CountGreaterThanToMILPBridge{T})
+    # * ExponentialConeToScalarNonlinearFunctionBridge{T}
+    #      This bridge is not added by default because it starts with a convex
+    #      conic constraint and adds a nonlinear constraint that local NLP
+    #      solvers like Ipopt can struggle with because of log(x) when x is 0.
+    #      In addition, the bridge does not support ConstraintDual.
+    #  * FunctionConversionBridge{T}
+    #      This bridge is not added because, even though it is not abstract, it
+    #      is highly parameterized, and parameterized versions such as
+    #      ScalarFunctionizeBridge are added.
+    MOI.Bridges.add_bridge(model, GeoMeanBridge{T})
+    MOI.Bridges.add_bridge(model, GeoMeanToPowerBridge{T})
+    MOI.Bridges.add_bridge(model, GeoMeantoRelEntrBridge{T})
+    if T <: AbstractFloat  # See note in docstring of AbstractToIntervalBridge
         MOI.Bridges.add_bridge(model, GreaterToIntervalBridge{T})
-        MOI.Bridges.add_bridge(model, LessToIntervalBridge{T})
     end
     MOI.Bridges.add_bridge(model, GreaterToLessBridge{T})
+    MOI.Bridges.add_bridge(model, HermitianToSymmetricPSDBridge{T})
+    MOI.Bridges.add_bridge(model, IndicatorActiveOnFalseBridge{T})
+    MOI.Bridges.add_bridge(model, IndicatorGreaterToLessThanBridge{T})
+    MOI.Bridges.add_bridge(model, IndicatorLessToGreaterThanBridge{T})
+    #  * IndicatorSetMapBridge{T}
+    #      This bridge is not added because, even though it is not abstract, it
+    #      is highly parameterized, and parameterized versions such as
+    #      IndicatorGreaterToLessThanBridge are added.
+    MOI.Bridges.add_bridge(model, IndicatorSOS1Bridge{T})
+    MOI.Bridges.add_bridge(model, IndicatorToMILPBridge{T})
+    #   * InequalityToComplementsBridge{T}
+    #       This bridge is not added because of a bug in Convex.jl:
+    #       https://github.com/jump-dev/Convex.jl/blob/ca5324217575af263bfeee20b3e0526bed051887/src/MOI_wrapper.jl#L119-L133
+    #       It is also really useful only to PATHSolver.jl, which could add this
+    #       to MOI.ListOfRequiredBridges.
+    MOI.Bridges.add_bridge(model, IntegerToZeroOneBridge{T})
     MOI.Bridges.add_bridge(model, LessToGreaterBridge{T})
+    if T <: AbstractFloat  # See note in docstring of AbstractToIntervalBridge
+        MOI.Bridges.add_bridge(model, LessToIntervalBridge{T})
+    end
+    MOI.Bridges.add_bridge(model, LogDetBridge{T})
     MOI.Bridges.add_bridge(model, NonnegToNonposBridge{T})
     MOI.Bridges.add_bridge(model, NonposToNonnegBridge{T})
-    MOI.Bridges.add_bridge(model, ScalarizeBridge{T})
-    MOI.Bridges.add_bridge(model, VectorizeBridge{T})
-    MOI.Bridges.add_bridge(model, ScalarSlackBridge{T})
-    MOI.Bridges.add_bridge(model, VectorSlackBridge{T})
-    MOI.Bridges.add_bridge(model, ScalarFunctionizeBridge{T})
-    MOI.Bridges.add_bridge(model, VectorFunctionizeBridge{T})
-    MOI.Bridges.add_bridge(model, ToScalarQuadraticBridge{T})
-    MOI.Bridges.add_bridge(model, ToVectorQuadraticBridge{T})
-    MOI.Bridges.add_bridge(model, ToScalarNonlinearBridge{T})
-    MOI.Bridges.add_bridge(model, SplitHyperRectangleBridge{T})
-    MOI.Bridges.add_bridge(model, SplitIntervalBridge{T})
-    MOI.Bridges.add_bridge(model, SplitComplexEqualToBridge{T})
-    MOI.Bridges.add_bridge(model, SplitComplexZerosBridge{T})
-    MOI.Bridges.add_bridge(model, QuadtoSOCBridge{T})
-    # We do not add `(R)SOCtoNonConvexQuad` because it starts with a convex
-    # conic constraint and generate a non-convex constraint (in the QCP
-    # interpretation).
     MOI.Bridges.add_bridge(model, NormInfinityBridge{T})
+    MOI.Bridges.add_bridge(model, NormInfinityConeToNormConeBridge{T})
+    MOI.Bridges.add_bridge(model, NormNuclearBridge{T})
     MOI.Bridges.add_bridge(model, NormOneBridge{T})
-    MOI.Bridges.add_bridge(model, GeoMeantoRelEntrBridge{T})
-    MOI.Bridges.add_bridge(model, GeoMeanBridge{T})
-    MOI.Bridges.add_bridge(model, GeoMeanToPowerBridge{T})
-    MOI.Bridges.add_bridge(model, NormToPowerBridge{T})
     MOI.Bridges.add_bridge(model, NormOneConeToNormConeBridge{T})
-    MOI.Bridges.add_bridge(model, SecondOrderConeToNormConeBridge{T})
-    MOI.Bridges.add_bridge(model, NormInfinityConeToNormConeBridge{T})
-    MOI.Bridges.add_bridge(model, ComplexNormInfinityToSecondOrderConeBridge{T})
-    MOI.Bridges.add_bridge(model, RelativeEntropyBridge{T})
+    #  * NormSpecialCaseBridge{T}
+    #      This bridge is not added because, even though it is not abstract, it
+    #      is highly parameterized, and parameterized versions such as
+    #      NormOneConeToNormConeBridge are added.
     MOI.Bridges.add_bridge(model, NormSpectralBridge{T})
-    MOI.Bridges.add_bridge(model, NormNuclearBridge{T})
-    MOI.Bridges.add_bridge(model, HermitianToSymmetricPSDBridge{T})
-    MOI.Bridges.add_bridge(model, SquareBridge{T})
-    MOI.Bridges.add_bridge(model, SetDotScalingBridge{T})
-    MOI.Bridges.add_bridge(model, SetDotInverseScalingBridge{T})
-    MOI.Bridges.add_bridge(model, LogDetBridge{T})
+    MOI.Bridges.add_bridge(model, NormToPowerBridge{T})
+    #  * NumberConversionBridge{T}
+    #      This bridge is not added by default because it would silently enable
+    #      models with mixed precision. In most cases, this is a bug in the
+    #      user's code, so we leave this bridge as opt-in.
+    MOI.Bridges.add_bridge(model, QuadtoSOCBridge{T})
+    MOI.Bridges.add_bridge(model, ReifiedAllDifferentToCountDistinctBridge{T})
+    MOI.Bridges.add_bridge(model, ReifiedCountDistinctToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, RelativeEntropyBridge{T})
     MOI.Bridges.add_bridge(model, RootDetBridge{T})
-    MOI.Bridges.add_bridge(model, RSOCtoSOCBridge{T})
-    MOI.Bridges.add_bridge(model, SOCtoRSOCBridge{T})
-    # We do not add `SOCtoPSDBridge` as transforming the `SOC` to `RSOC` and
-    # then to `PSD` produces a smaller SDP constraint.
-    # MOI.Bridges.add_bridge(model, SOCtoPSDBridge{T})
+    #  * RSOCtoNonConvexQuadBridge{T}
+    #      This bridge is not added by default because it starts with a convex
+    #      conic constraint and generate a non-convex constraint (in the QCP
+    #      interpretation).
     MOI.Bridges.add_bridge(model, RSOCtoPSDBridge{T})
-    MOI.Bridges.add_bridge(model, IndicatorActiveOnFalseBridge{T})
-    MOI.Bridges.add_bridge(model, IndicatorSOS1Bridge{T})
-    MOI.Bridges.add_bridge(model, IndicatorLessToGreaterThanBridge{T})
-    MOI.Bridges.add_bridge(model, IndicatorGreaterToLessThanBridge{T})
+    MOI.Bridges.add_bridge(model, RSOCtoSOCBridge{T})
+    MOI.Bridges.add_bridge(model, ScalarFunctionizeBridge{T})
+    MOI.Bridges.add_bridge(model, ScalarizeBridge{T})
+    MOI.Bridges.add_bridge(model, ScalarSlackBridge{T})
+    MOI.Bridges.add_bridge(model, SecondOrderConeToNormConeBridge{T})
     MOI.Bridges.add_bridge(model, SemiToBinaryBridge{T})
-    MOI.Bridges.add_bridge(model, ZeroOneBridge{T})
-    MOI.Bridges.add_bridge(model, IntegerToZeroOneBridge{T})
-    MOI.Bridges.add_bridge(model, InequalityToComplementsBridge{T})
-    # Do not add by default
-    # MOI.Bridges.add_bridge(model, NumberConversionBridge{T})
-    # Constraint programming bridges
-    MOI.Bridges.add_bridge(model, AllDifferentToCountDistinctBridge{T})
-    MOI.Bridges.add_bridge(model, ReifiedAllDifferentToCountDistinctBridge{T})
-    MOI.Bridges.add_bridge(model, BinPackingToMILPBridge{T})
-    MOI.Bridges.add_bridge(model, CircuitToMILPBridge{T})
-    MOI.Bridges.add_bridge(model, CountAtLeastToCountBelongsBridge{T})
-    MOI.Bridges.add_bridge(model, CountBelongsToMILPBridge{T})
-    MOI.Bridges.add_bridge(model, CountDistinctToMILPBridge{T})
-    MOI.Bridges.add_bridge(model, ReifiedCountDistinctToMILPBridge{T})
-    MOI.Bridges.add_bridge(model, CountGreaterThanToMILPBridge{T})
-    MOI.Bridges.add_bridge(model, TableToMILPBridge{T})
+    #  * SetConversionBridge{T}
+    #      This bridge is not added because, even though it is not abstract, it
+    #      is highly parameterized, and it intended for use by MOI extensions.
+    MOI.Bridges.add_bridge(model, SetDotInverseScalingBridge{T})
+    MOI.Bridges.add_bridge(model, SetDotScalingBridge{T})
+    #  * SOCtoNonConvexQuadBridge{T}
+    #      This bridge is not added by default because it starts with a convex
+    #      conic constraint and generate a non-convex constraint (in the QCP
+    #      interpretation).
+    #  * SOCtoPSDBridge{T}
+    #      This bridge is not added because transforming the `SOC` to `RSOC` and
+    #      then to `PSD` produces a smaller SDP constraint. `RSOCtoPSDBridge` is
+    #      added by default.
+    MOI.Bridges.add_bridge(model, SOCtoRSOCBridge{T})
     MOI.Bridges.add_bridge(model, SOS1ToMILPBridge{T})
     MOI.Bridges.add_bridge(model, SOS2ToMILPBridge{T})
-    MOI.Bridges.add_bridge(model, IndicatorToMILPBridge{T})
-    MOI.Bridges.add_bridge(
-        model,
-        ExponentialConeToScalarNonlinearFunctionBridge{T},
-    )
+    MOI.Bridges.add_bridge(model, SplitComplexEqualToBridge{T})
+    MOI.Bridges.add_bridge(model, SplitComplexZerosBridge{T})
+    MOI.Bridges.add_bridge(model, SplitHyperRectangleBridge{T})
+    MOI.Bridges.add_bridge(model, SplitIntervalBridge{T})
+    MOI.Bridges.add_bridge(model, SquareBridge{T})
+    MOI.Bridges.add_bridge(model, TableToMILPBridge{T})
+    MOI.Bridges.add_bridge(model, ToScalarNonlinearBridge{T})
+    MOI.Bridges.add_bridge(model, ToScalarQuadraticBridge{T})
+    MOI.Bridges.add_bridge(model, ToVectorQuadraticBridge{T})
+    MOI.Bridges.add_bridge(model, VectorFunctionizeBridge{T})
+    MOI.Bridges.add_bridge(model, VectorizeBridge{T})
+    MOI.Bridges.add_bridge(model, VectorSlackBridge{T})
+    MOI.Bridges.add_bridge(model, ZeroOneBridge{T})
     return
 end
 

src/Bridges/Constraint/bridges/SOCtoPSDBridge.jl

@@ -77,6 +77,11 @@
 const SOCtoPSD{T,OT<:MOI.ModelLike} =
     SingleBridgeOptimizer{SOCtoPSDBridge{T},OT}
 
+# This bridge destorys a lot of structure and adding PSD variables is almost
+# always undesirable. We give this bridge a high cost so that it is used only if
+# necessary.
+MOI.Bridges.bridging_cost(::Type{<:SOCtoPSDBridge}) = 10.0
+
 function concrete_bridge_type(
     ::Type{<:SOCtoPSDBridge{T}},
     G::Type{<:MOI.AbstractVectorFunction},
@@ -186,6 +191,11 @@
 const RSOCtoPSD{T,OT<:MOI.ModelLike} =
     SingleBridgeOptimizer{RSOCtoPSDBridge{T},OT}
 
+# This bridge destorys a lot of structure and adding PSD variables is almost
+# always undesirable. We give this bridge a high cost so that it is used only if
+# necessary.
+MOI.Bridges.bridging_cost(::Type{<:RSOCtoPSDBridge}) = 10.0
+
 function concrete_bridge_type(
     ::Type{<:RSOCtoPSDBridge{T}},
     G::Type{<:MOI.AbstractVectorFunction},

src/Bridges/Variable/bridges/RSOCtoPSDBridge.jl

@@ -57,8 +57,8 @@ const RSOCtoPSD{T,OT<:MOI.ModelLike} =
     SingleBridgeOptimizer{RSOCtoPSDBridge{T},OT}
 
 # This bridge destorys a lot of structure and adding PSD variables is almost
-# always undesirable. We give this bridge an arbitrarily hight cost so that it
-# is used only if necessary.
+# always undesirable. We give this bridge a high cost so that it is used only if
+# necessary.
 MOI.Bridges.bridging_cost(::Type{<:RSOCtoPSDBridge}) = 10.0
 
 function bridge_constrained_variable(

test/Bridges/Constraint/SOCtoPSDBridge.jl

@@ -211,6 +211,26 @@ function test_runtests()
     return
 end
 
+function test_bridging_cost_SOCtoPSD()
+    inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
+    model = MOI.Bridges.Constraint.SOCtoPSD{Float64}(inner)
+    x = MOI.add_variables(model, 3)
+    c = MOI.add_constraint(model, x, MOI.SecondOrderCone(3))
+    bridge = model.map[c]
+    MOI.Bridges.bridging_cost(typeof(bridge)) == 10.0
+    return
+end
+
+function test_bridging_cost_RSOCtoPSD()
+    inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
+    model = MOI.Bridges.Constraint.RSOCtoPSD{Float64}(inner)
+    x = MOI.add_variables(model, 3)
+    c = MOI.add_constraint(model, x, MOI.RotatedSecondOrderCone(3))
+    bridge = model.map[c]
+    MOI.Bridges.bridging_cost(typeof(bridge)) == 10.0
+    return
+end
+
 end  # module
 
 TestConstraintSOCtoPSD.runtests()

test/Bridges/bridge_optimizer.jl

@@ -567,6 +567,20 @@ function test_double_deletion_scalar()
     # careful not to delete the second one twice, see https://github.com/jump-dev/MathOptInterface.jl/issues/1231
     model =
         MOI.instantiate(AffineOnlyModel{Float64}, with_bridge_type = Float64)
+    # If LessToGreaterBridge exists, this goes from:
+    #   VariableIndex(x) in LessThan(1.0)
+    #   ScalarAffineFunction(-1.0x) in GreaterThan(-1.0)     (LessToGreater)
+    #   ScalarAffineFunction(-1.0x) in Interval(-1.0, Inf)   (GreaterToInterval)
+    # we want instead
+    #   VariableIndex(x) in LessThan(1.0)
+    #   VariableIndex(x) in Interval(-Inf, 1.0)             (LessToInterval)
+    #   ScalarAffineFunction(1.0x) in Interval(-Inf, 1.0)   (FunctionConversion)
+    # To check that we handle the LessThan and Interval sets on the same
+    # VariableIndex correctly.
+    MOI.Bridges.remove_bridge(
+        model,
+        MOI.Bridges.Constraint.LessToGreaterBridge{Float64},
+    )
     x = MOI.add_variable(model)
     c = MOI.add_constraint(model, x, MOI.LessThan(1.0))
     # Need to test the bridging to make sure it's not functionized first as otherwise,

test/Bridges/lazy_bridge_optimizer.jl

@@ -1704,7 +1704,6 @@ function test_MOI_runtests_No_RSOCModel()
     return
 end
 
-# Test that RSOCtoPSD is used instead of RSOC+SOCtoPSD as it is a shortest path.
 function test_bridge_selection()
     mock = MOI.Utilities.MockOptimizer(NoRSOCModel{Float64}())
     bridged_mock = MOI.Bridges.LazyBridgeOptimizer(mock)
@@ -1751,13 +1750,13 @@ function test_bridge_selection()
         bridged_mock,
         MOI.VectorOfVariables,
         MOI.RotatedSecondOrderCone,
-    ) == MOI.Bridges.Constraint.RSOCtoPSDBridge{
+    ) == MOI.Bridges.Constraint.RSOCtoSOCBridge{
         Float64,
         MOI.VectorAffineFunction{Float64},
         MOI.VectorOfVariables,
     }
     @test MOI.Bridges.bridge(bridged_mock, c) isa
-          MOI.Bridges.Constraint.RSOCtoPSDBridge
+          MOI.Bridges.Constraint.RSOCtoSOCBridge
     @test bridged_mock.graph.constraint_dist[MOI.Bridges.node(
         bridged_mock,
         MOI.VectorOfVariables,