Feature request: general numeric types

[ericphanson]

It would be great if Dualization could support generic numeric types. It looks like some effort was made towards that with the DualOptimizer{T} constructor, but there's a lot of hardcoded Float64's that cause errors like

ERROR: MathOptInterface.UnsupportedConstraint{MathOptInterface.VectorAffineFunction{BigFloat},MathOptInterface.PositiveSemidefiniteConeTriangle}: `MathOptInterface.VectorAffineFunction{BigFloat}`-in-`MathOptInterface.PositiveSemidefiniteConeTriangle` constraint is not supported by the model.

An example problem is

using Convex, GenericLinearAlgebra, Dualization, SDPAFamily
f = Convex.ProblemDepot.PROBLEMS["sdp"]["sdp_nuclear_norm_atom"]
T=BigFloat
f(Val(true), 1e-3, 0, T) do p
       solve!(p, DualOptimizer{T}(SDPAFamily.Optimizer{T}(presolve=true)))
 end

which errors with T=BigFloat and succeeds with T=Float64 (using release versions of each package).

Full stacktrace (with T=BigFloat)

julia> f(Val(true), 1e-3, 0, T) do p
       solve!(p, DualOptimizer{T}(SDPAFamily.Optimizer{T}(presolve=true)))
       end
ERROR: MathOptInterface.UnsupportedConstraint{MathOptInterface.VectorAffineFunction{BigFloat},MathOptInterface.PositiveSemidefiniteConeTriangle}: `MathOptInterface.VectorAffineFunction{BigFloat}`-in-`MathOptInterface.PositiveSemidefiniteConeTriangle` constraint is not supported by the model.
Stacktrace:
 [1] bridge_type(::MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{DualOptimizer{BigFloat,MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SDPAFamily.Optimizer{BigFloat},Dualization.DualizableModel{BigFloat}}}},MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{BigFloat}}}}, ::Type{MathOptInterface.VectorAffineFunction{BigFloat}}, ::Type{MathOptInterface.PositiveSemidefiniteConeTriangle}) at /Users/eh540/.julia/packages/MathOptInterface/XiH8D/src/Bridges/lazy_bridge_optimizer.jl:330
 [2] concrete_bridge_type(::MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{DualOptimizer{BigFloat,MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SDPAFamily.Optimizer{BigFloat},Dualization.DualizableModel{BigFloat}}}},MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{BigFloat}}}}, ::Type{MathOptInterface.VectorAffineFunction{BigFloat}}, ::Type{MathOptInterface.PositiveSemidefiniteConeTriangle}) at /Users/eh540/.julia/packages/MathOptInterface/XiH8D/src/Bridges/Constraint/bridge.jl:120
 [3] add_constraint(::MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{DualOptimizer{BigFloat,MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SDPAFamily.Optimizer{BigFloat},Dualization.DualizableModel{BigFloat}}}},MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{BigFloat}}}}, ::MathOptInterface.VectorAffineFunction{BigFloat}, ::MathOptInterface.PositiveSemidefiniteConeTriangle) at /Users/eh540/.julia/packages/MathOptInterface/XiH8D/src/Bridges/bridge_optimizer.jl:1052
 [4] _broadcast_getindex_evalf(::typeof(MathOptInterface.add_constraint), ::MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{DualOptimizer{BigFloat,MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SDPAFamily.Optimizer{BigFloat},Dualization.DualizableModel{BigFloat}}}},MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{BigFloat}}}}, ::MathOptInterface.VectorAffineFunction{BigFloat}, ::MathOptInterface.PositiveSemidefiniteConeTriangle) at ./broadcast.jl:630
 [5] _broadcast_getindex at ./broadcast.jl:603 [inlined]
 [6] getindex at ./broadcast.jl:563 [inlined]
 [7] copy at ./broadcast.jl:853 [inlined]
 [8] materialize at ./broadcast.jl:819 [inlined]
 [9] add_constraints(::MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{DualOptimizer{BigFloat,MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SDPAFamily.Optimizer{BigFloat},Dualization.DualizableModel{BigFloat}}}},MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{BigFloat}}}}, ::Array{Union{MathOptInterface.SingleVariable, MathOptInterface.VectorAffineFunction{BigFloat}},1}, ::Array{Any,1}) at /Users/eh540/.julia/packages/MathOptInterface/XiH8D/src/constraints.jl:175
 [10] load_MOI_model!(::MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{DualOptimizer{BigFloat,MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SDPAFamily.Optimizer{BigFloat},Dualization.DualizableModel{BigFloat}}}},MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{BigFloat}}}}, ::Problem{BigFloat}) at /Users/eh540/.julia/packages/Convex/IJj5u/src/solution.jl:186
 [11] #solve!#15(::Bool, ::Bool, ::Bool, ::typeof(solve!), ::Problem{BigFloat}, ::DualOptimizer{BigFloat,MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SDPAFamily.Optimizer{BigFloat},Dualization.DualizableModel{BigFloat}}}}) at /Users/eh540/.julia/packages/Convex/IJj5u/src/solution.jl:216
 [12] solve!(::Problem{BigFloat}, ::DualOptimizer{BigFloat,MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SDPAFamily.Optimizer{BigFloat},Dualization.DualizableModel{BigFloat}}}}) at /Users/eh540/.julia/packages/Convex/IJj5u/src/solution.jl:204
 [13] (::var"#21#22")(::Problem{BigFloat}) at ./REPL[43]:2
 [14] sdp_nuclear_norm_atom(::var"#21#22", ::Val{true}, ::Float64, ::Int64, ::Type{BigFloat}) at /Users/eh540/.julia/packages/Convex/IJj5u/src/problem_depot/problems/sdp.jl:80
 [15] top-level scope at REPL[43]:1