Improve error messages of various errors

[odow]

I might break out the UnsupportedConstraint into a separate PR, but I'll see the damage here first.

[odow]

Motivated by jump-dev/Dualization.jl#232

julia> using LinearAlgebra

julia> using Hypatia

julia> using Dualization

julia> using JuMP

julia> 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
test_dual (generic function with 1 method)

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:

[odow]

cc @araujoms

[araujoms]

Suggested change

	constraint into a form supported by the solver.
	The model that we were unable to add the constraint to is:
	$(sprint(show, model))
	constraint into a form supported by the solver $(sprint(show, MOI.get(model, MOI.SolverName())))

I'd just print the solver name instead of the whole model, since the solver is what makes the constraint unsupported.

[odow]

So this isn't print(model), but it's show(model). Which is the high level summary.

[araujoms]

Which still has a lot of irrelevant information.

[odow]

SolverName drops a lot of relevant information.

julia> MOI.get(b, MOI.SolverName())
"Dual model with Hypatia attached"

It looks through the bridging layer and the cache.

[araujoms]

I know this is the result, it's exactly the information I wanted to have, which is why I suggested it.

It's just a suggestion, feel free to ignore it.

[odow]

@araujoms here you go

[odow]

https://github.com/jump-dev/MathOptInterface.jl/actions/runs/30490632040

[blegat]

Nice improvements