Issue when differentiating a semi-definite program

[frapac]

I got a weird issue if I try to compute the sensitivity from the following SDP:

using JuMP
using DiffOpt
using Clarabel

model = Model(() -> DiffOpt.diff_optimizer(Clarabel.Optimizer))
@variable(model , t >= 0)
cons = @constraint(model , [t 1.0 ; 1.0 t] in PSDCone())
@objective(model, Min , t)
optimize!(model)

MOI.set(model, DiffOpt.ForwardConstraintFunction(), cons, [1.0 0.0; 0.0 1.0])
DiffOpt.forward_differentiate!(model) 

The code returns the following error saying the optimizer has not been called (which is not the case here as we are calling optimize! just before computing the sensitivity):

ERROR: LoadError: Trying to compute the forward differentiation on a model with termination status OPTIMIZE_NOT_CALLED
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:35
 [2] forward_differentiate!(model::DiffOpt.Optimizer{MathOptInterface.Utilities.CachingOptimizer{…}})
   @ DiffOpt ~/.julia/packages/DiffOpt/FJjnq/src/moi_wrapper.jl:553
 [3] forward_differentiate!
   @ ~/.julia/packages/DiffOpt/FJjnq/src/jump_moi_overloads.jl:393 [inlined]
 [4] forward_differentiate!(model::MathOptInterface.Utilities.CachingOptimizer{…})
   @ DiffOpt ~/.julia/packages/DiffOpt/FJjnq/src/jump_moi_overloads.jl:378
 [5] forward_differentiate!(model::Model)
   @ DiffOpt ~/.julia/packages/DiffOpt/FJjnq/src/jump_moi_overloads.jl:363

If I look at the unit-tests implemented in DiffOpt, I observe that the error can be resolved if use instead the following hack:

using JuMP
using DiffOpt
using Clarabel

model = Model(() -> DiffOpt.diff_optimizer(Clarabel.Optimizer))
@variable(model , t >= 0)
cons = @constraint(model , [t 1.0 ; 1.0 t] in PSDCone())
@objective(model, Min , t)
optimize!(model)

h = MOI.VectorAffineFunction{Float64}(
            MOI.ScalarAffineTerm{Float64}[],
            ones(3),
)
MOI.set(model, DiffOpt.ForwardConstraintFunction(), cons, h)
DiffOpt.forward_differentiate!(model)

but even when doing that, I got a second error saying the dual of a PSD cone does not exist (I guess the error is somewhat related to MathOptSetDistances):

ERROR: LoadError: Dual of `PositiveSemidefiniteConeSquare` is not defined in MathOptInterface.
For more details see the comments in `src/Bridges/Constraint/bridges/square.jl`.
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] dual_set(::MathOptInterface.PositiveSemidefiniteConeSquare)
    @ MathOptInterface ~/.julia/packages/MathOptInterface/eRhCr/src/sets.jl:1296
  [3] (::DiffOpt.var"#14#15"{…})(ci::MathOptInterface.ConstraintIndex{…}, r::UnitRange{…})
    @ DiffOpt ~/.julia/packages/DiffOpt/FJjnq/src/diff_opt.jl:512
  [4] _map_rows!(f::DiffOpt.var"#14#15"{…}, x::Vector{…}, model::MathOptInterface.Utilities.GenericModel{…}, cones::DiffOpt.ProductOfSets{…}, ::Type{…}, ::Type{…}, map_mode::DiffOpt.Nested{…}, k::Int64)
    @ DiffOpt ~/.julia/packages/DiffOpt/FJjnq/src/diff_opt.jl:550
  [5] map_rows(f::Function, model::MathOptInterface.Utilities.GenericModel{…}, cones::DiffOpt.ProductOfSets{…}, map_mode::DiffOpt.Nested{…})
    @ DiffOpt ~/.julia/packages/DiffOpt/FJjnq/src/diff_opt.jl:589
  [6] Dπ
    @ ~/.julia/packages/DiffOpt/FJjnq/src/diff_opt.jl:510 [inlined]
  [7] _gradient_cache(model::DiffOpt.ConicProgram.Model)
    @ DiffOpt.ConicProgram ~/.julia/packages/DiffOpt/FJjnq/src/ConicProgram/ConicProgram.jl:225

Do you have any clue on how to resolve this issue? If I am not using DiffOpt.jl correctly, I would be happy to write a new paragraph in the documentation that explains how to compute the sensitivity from a PSDCone.

[odow]

This is the same question as https://discourse.julialang.org/t/differentiate-through-secondordercone/130365

[joaquimg]

I will push an update in #281 this weekend that might help with this

[joaquimg]

The issue is not correlated to my PR, but I think it is just a matter of adding:

function MOI.supports_constraint(
    ::Model,
    ::Type{MOI.VectorAffineFunction{T}},
    ::Type{MOI.PositiveSemidefiniteConeSquare},
) where {T}
    return false
end

to the ConicProgram.jl file.