Can't dualize exotic cone

[araujoms]

When trying to dualize a conic problem involving Hypatia's EpiNormSpectralTriCone I get the following error message

ERROR: UnsupportedConstraint: `MathOptInterface.VectorAffineFunction{Float64}`-in-`EpiNormSpectralTriCone{Float64, Float64}` 
constraints are not supported by the solver you have chosen, and we could not reformulate your model into a
form that is supported.

To fix this error you must choose a different solver.

which is clearly incorrect. I don't know if this is a bug in Hypatia or Dualization, though, or more generally how can Dualization even know what the dual of this cone is. MWE:

using LinearAlgebra
using Hypatia
using Dualization
using JuMP

function test_dual()
    model = Model()
    @variable(model, M[1:2, 1:2], Symmetric)
    @constraint(model, [1, M[1, 1], sqrt(2) * M[1, 2], M[2, 2]] in Hypatia.EpiNormSpectralTriCone{Float64,Float64}(1 + 3))
    @objective(model, Max, real(tr(M)))
    #set_optimizer(model, Hypatia.Optimizer)
    set_optimizer(model, Dualization.dual_optimizer(Hypatia.Optimizer))
    optimize!(model)
    return value(M)
end

[odow]

This seems like everything is working as intended?

Dualization.Optimizer doesn't know how to dualise the constraint MathOptInterface.VectorAffineFunction{Float64}-in-EpiNormSpectralTriCone{Float64, Float64}.

What would you expect to happen? Is this just a request for a better error message when Dualization fails?

[araujoms]

A correct error message would certainly be an improvement, but what I actually want is to dualize the problem. Is there any documentation that explains how to teach Dualization to dualize new cones?

[odow]

You need to implement MOI.dual_set and MOI.dual_set_type.

https://jump.dev/JuMP.jl/stable/moi/reference/standard_form/#MathOptInterface.dual_set

https://jump.dev/JuMP.jl/stable/moi/reference/standard_form/#MathOptInterface.dual_set_type

[odow]

Part of the problem is that Dualization is just saying "I don't support that" instead of some more specific error:

Dualization.jl/src/supported.jl

Lines 43 to 55 in 29fb61f

	function supported_constraint(
	::Type{<:Union{MOI.VariableIndex,MOI.ScalarAffineFunction}},
	S::Type{<:MOI.AbstractScalarSet},
	)
	return _dual_set_type(S) !== nothing
	end
	function supported_constraint(
	::Type{<:Union{MOI.VectorOfVariables,MOI.VectorAffineFunction}},
	S::Type{<:MOI.AbstractVectorSet},
	)
	return _dual_set_type(S) !== nothing
	end

[odow]

Closing because there's nothing to do here in Dualization.jl. I'm taking a look to see if we can improve the error messages in MOI.

[araujoms]

Thanks, that works:

MOI.dual_set(c::Hypatia.EpiNormSpectralTriCone{T,R}) where {T,R} =
    Hypatia.EpiNormSpectralTriCone{T,R}(MOI.dimension(c), !c.use_dual)
MOI.dual_set_type(T::Type{<:Hypatia.EpiNormSpectralTriCone}) = T

The documentation seems outdated, though, it claims that Dualization.supported_constraint is necessary and doesn't mention MOI.dual_set_type: https://jump.dev/Dualization.jl/stable/manual/#Advanced:-add-support-for-new-sets

[odow]

Actually, we can improve https://jump.dev/Dualization.jl/stable/manual/#Advanced:-add-support-for-new-sets

[odow]

Yeah I just noticed that too haha

[araujoms]

I think I understood the problem: from MOI's point of view the solver is not Hypatia, but Dualization.dual_optimizer, which in fact does not support this type of constraint. Perhaps the error message could include what the solver is? That would make it clear.

[odow]

I'll see what I can do. It'll need to happen in MOI, not Dualization.

[odow]

How about something like:

julia> test_dual()
ERROR: UnsupportedConstraint{
    MathOptInterface.VectorAffineFunction{Float64},
    EpiNormSpectralTriCone{Float64, Float64},
}

This constraint type is not supported by the solver.

To fix this error you must choose a different solver.

## More information

Bridges are enabled, but there are none that can rewrite the constraint into a form supported by the solver.

The model that we were unable to add the constraint to is:

MOIB.LazyBridgeOptimizer{MOIU.CachingOptimizer{DualOptimizer{Float64, MOIB.LazyBridgeOptimizer{MOIU.CachingOptimizer{Hypatia.Optimizer{Float64}, MOIU.UniversalFallback{MOIU.Model{Float64}}}}}, MOIU.UniversalFallback{MOIU.Model{Float64}}}}
├ Variable bridges: none
├ Constraint bridges: none
├ Objective bridges: none
└ model: MOIU.CachingOptimizer
  ├ state: EMPTY_OPTIMIZER
  ├ mode: AUTOMATIC
  ├ model_cache: MOIU.UniversalFallback{MOIU.Model{Float64}}
  │ ├ ObjectiveSense: MAX_SENSE
  │ ├ ObjectiveFunctionType: MOI.ScalarAffineFunction{Float64}
  │ ├ NumberOfVariables: 3
  │ └ NumberOfConstraints: 0
  └ optimizer: DualOptimizer{Float64, MOIB.LazyBridgeOptimizer{MOIU.CachingOptimizer{Hypatia.Optimizer{Float64}, MOIU.UniversalFallback{MOIU.Model{Float64}}}}}
    ├ ObjectiveSense: unknown
    ├ ObjectiveFunctionType: unknown
    ├ NumberOfVariables: unknown
    └ NumberOfConstraints: unknown

Stacktrace: