Add support for starting values in bridges

[blegat]

Updated list

Constraint Bridge	ConstraintPrimal	ConstraintDual
GreaterToIntervalBridge	x	x
LessToIntervalBridge	x	x
GreaterToLessBridge	x	x
LessToGreaterBridge	x	x
NonnegToNonposBridge	x	x
NonposToNonnegBridge	x	x
VectorizeBridge	x	x
ScalarizeBridge	x	x
ScalarSlackBridge	x	x
VectorSlackBridge	x	x
ScalarFunctionizeBridge	x	x
VectorFunctionizeBridge	x	x
SplitComplexEqualToBridge	x	x
SplitComplexZerosBridge	x	x
SplitIntervalBridge	x	x
SOCtoRSOCBridge	x	x
RSOCtoSOCBridge	x	x
SOCtoNonConvexQuadBridge	NA	NA
RSOCtoNonConvexQuadBridge	NA	NA
QuadtoSOCBridge	NA	NA
SOCtoPSDBridge
RSOCtoPSDBridge
NormInfinityBridge	x	x
NormOneBridge	x	x
GeoMeantoRelEntrBridge	x	x
GeoMeanBridge
RelativeEntropyBridge	x	x
NormSpectralBridge
NormNuclearBridge	x	x
SquareBridge
RootDetBridge
LogDetBridge	x	x
IndicatorActiveOnFalseBridge	NA	NA
IndicatorSOS1Bridge	NA	NA
SemiToBinaryBridge	NA	NA
ZeroOneBridge	NA	NA
AllDifferentToCountDistinctBridge	NA	NA
BinPackingToMILPBridge	NA	NA
CircuitToMILPBridge	NA	NA
CountAtLeastToCountBelongsBridge	NA	NA
CountBelongsToMILPBridge	NA	NA
CountDistinctToMILPBridge	NA	NA
CountGreaterThanToMILPBridge	NA	NA
TableToMILPBridge	NA	NA

Variable Bridge	VariablePrimal	ConstraintPrimal	ConstraintDual
FreeBridge	x
NonposToNonnegBridge	x
RSOCtoPSDBridge
RSOCtoSOCBridge
SOCtoRSOCBridge
VectorizeBridge	x
ZerosBridge

[odow]

Another missing one is square to triangular PSD matrices: https://github.com/jump-dev/MathOptInterface.jl/issues/1730

[odow]

Updated list

Bridge	Constraint Primal	Constraint Dual
GreaterToIntervalBridge	x	x
LessToIntervalBridge	x	x
GreaterToLessBridge	x	x
LessToGreaterBridge	x	x
NonnegToNonposBridge	x	x
NonposToNonnegBridge	x	x
VectorizeBridge	x	x
ScalarizeBridge	x	x
ScalarSlackBridge	x	x
VectorSlackBridge	x	x
ScalarFunctionizeBridge	x	x
VectorFunctionizeBridge	x	x
SplitComplexEqualToBridge	x	x
SplitComplexZerosBridge	x	x
SplitIntervalBridge	x	x
SOCtoRSOCBridge
RSOCtoSOCBridge
SOCtoNonConvexQuadBridge
RSOCtoNonConvexQuadBridge
QuadtoSOCBridge
SOCtoPSDBridge
RSOCtoPSDBridge
NormInfinityBridge	x	x
NormOneBridge	x	x
GeoMeantoRelEntrBridge	x	x
GeoMeanBridge
RelativeEntropyBridge	x	x
NormSpectralBridge
NormNuclearBridge	x	x
SquareBridge
RootDetBridge
LogDetBridge	x	x
IndicatorActiveOnFalseBridge	NA	NA
IndicatorSOS1Bridge	NA	NA
SemiToBinaryBridge	NA	NA
ZeroOneBridge	NA	NA
AllDifferentToCountDistinctBridge	NA	NA
BinPackingToMILPBridge	NA	NA
CircuitToMILPBridge	NA	NA
CountAtLeastToCountBelongsBridge	NA	NA
CountBelongsToMILPBridge	NA	NA
CountDistinctToMILPBridge	NA	NA
CountGreaterThanToMILPBridge	NA	NA
TableToMILPBridge	NA	NA

Bridge	VariablePrimal	ConstraintPrimal	ConstraintDual
FreeBridge	x
NonposToNonnegBridge	x
RSOCtoPSDBridge
RSOCtoSOCBridge
SOCtoRSOCBridge
VectorizeBridge	x
ZerosBridge

[odow]

function get_unsupported_bridges()
    dict = Dict{String,Vector{String}}()
    for attr in ("VariablePrimalStart", "ConstraintPrimalStart", "ConstraintDualStart")
        ret = String[]
        for t in ("Constraint", "Objective", "Variable")
            dir = "src/Bridges/$t/bridges"
            for file in readdir(dir)
                filename = joinpath(dir, file)
                contents = read(filename, String)
                if occursin("SetMapBridge", contents)
                    continue
                end
                if !occursin("::MOI.$attr", contents)
                    push!(ret, filename)
                end
            end
        end
        dict[attr] = ret
    end
    return dict
end
dict = get_unsupported_bridges()

Then with a bit of manual culling, I thing we can get things down to:

julia> dict["ConstraintPrimalStart"]
31-element Vector{String}:
 "src/Bridges/Constraint/bridges/det.jl"
 "src/Bridges/Constraint/bridges/geomean.jl"
 "src/Bridges/Constraint/bridges/norm_to_power.jl"
 "src/Bridges/Constraint/bridges/number_conversion.jl"
 "src/Bridges/Constraint/bridges/soc_to_nonconvex_quad.jl"
 "src/Bridges/Constraint/bridges/square.jl"

julia> dict["ConstraintDualStart"]
33-element Vector{String}:
 "src/Bridges/Constraint/bridges/det.jl"
 "src/Bridges/Constraint/bridges/geomean.jl"
 "src/Bridges/Constraint/bridges/norm_to_power.jl"
 "src/Bridges/Constraint/bridges/number_conversion.jl"
 "src/Bridges/Constraint/bridges/soc_to_nonconvex_quad.jl"
 "src/Bridges/Constraint/bridges/square.jl"

julia> dict["VariablePrimalStart"]
44-element Vector{String}:
 "src/Bridges/Variable/bridges/parameter.jl"
 "src/Bridges/Variable/bridges/rsoc_to_psd.jl"

[odow]

With the latest PRs (and excluding src/Bridges/Constraint/bridges/soc_to_nonconvex_quad.jl), we're down to

julia> dict["ConstraintPrimalStart"]
31-element Vector{String}:
 "src/Bridges/Constraint/bridges/det.jl"
 "src/Bridges/Constraint/bridges/geomean.jl"
 "src/Bridges/Constraint/bridges/norm_to_power.jl"

julia> dict["ConstraintDualStart"]
33-element Vector{String}:
 "src/Bridges/Constraint/bridges/det.jl"
 "src/Bridges/Constraint/bridges/geomean.jl"
 "src/Bridges/Constraint/bridges/norm_to_power.jl"

[odow]

But actually, the LogDet bridge does support starting values. And the geo-mean and norm bridge are niche enough that there isn't a big drive. They're also slightly complicated to work out the duals for?

So maybe this issue can be closed. There's still the unresolved https://github.com/jump-dev/MathOptInterface.jl/issues/2117.

And since there's a better error message telling people to open an issue if they hit a case that isn't implemented, we can re-open if there is demand.

[odow]

@blegat are you ready to close this?

[blegat]

There are still a few missing

[odow]

Sure. But are they useful? We have an error message telling people to open an issue, and no one has :smile:

[blegat]

I think we're good, these are not the only attributes not implemented by bridges