REDUCTION_CERTIFICATE

[blegat]

We removed it as we thought it was dropped from Mosek (see #575 (comment)) but I often still get it (with Mosek v8), i.e. these lines are executed:
https://github.com/JuliaOpt/MosekTools.jl/blob/d274a8381b6548f5ef25ad249e28884a6a557fed/src/attributes.jl#L494
https://github.com/JuliaOpt/MosekTools.jl/blob/d274a8381b6548f5ef25ad249e28884a6a557fed/src/attributes.jl#L519
and I get an Undefined error since it was removed from MOI.

@ulfworsoe @erling-d-andersen Was this feature removed in Mosek v9 ?

[erling-d-andersen]

I am not sure who did

elseif solsta == MSK_SOL_STA_PRIM_ILLPOSED_CER
MOI.NO_SOLUTION
elseif solsta == MSK_SOL_STA_DUAL_ILLPOSED_CER
MOI.REDUCTION_CERTIFICATE

Why do say no solution in one case and certificate in the other. To me it makes zero sense.

Both solution statuses are of course still possible.

In v9 we removed all the statuses that something with NEAR in them.

[blegat]

Thank you for the quick reply!

Why do say no solution in one case and certificate in the other

For MSK_SOL_STA_PRIM_ILLPOSED_CER, the MOI.PrimalStatus is MOI.NO_SOLUTION and the MOI.DualStatus is MOI.REDUCTION_CERTIFICATE because the certificate is contained in the dual solution and there is no primal solution. This is similar to MSK_SOL_STA_PRIM_INFEAS_CER where there is no primal solution and the dual contains an infeasibility ray.

[erling-d-andersen]

Got the logic now i.e. separate primal and dual statuses. Good solution.

[erling-d-andersen]

Btw if you see ill posed then you most likely have nasty model. Not that I cannot exclude a bug, but I would be worried about seeing illposed.

[blegat]

Btw if you see ill posed then you most likely have nasty model.

Indeed, it is nasty by design. This is a model parametrized by some parameter γ. For γ < γ*, it is infeasible and for γ > γ*, it is feasible. I am doing bisection to find γ*.
https://github.com/blegat/SwitchOnSafety.jl/blob/a0b3e6de04e477a44e70bdb374d987620f8a736c/src/sos.jl#L217-L294
For some interval around γ*, the problem is ill conditioned and the solver fails to determine whether the problem is feasible or not.

[erling-d-andersen]

It is a hard one.