Hypatia.jl

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implement more complete conic algorithm that can return unbounded certificates and distinguish primal or dual infeasibility

1

solves auxiliary conic problems if necessary, with some zeroed-out b, c, or h. see https://epubs.siam.org/doi/pdf/10.1137/15M1049415

chriscoey

detect primal vs dual facial reduction certificate and return appropriate MOI status

3

`MOI.ReductionCertificate`, `MOI.NearlyReductionCertificate` see this [reference](https://epubs.siam.org/doi/pdf/10.1137/15M1049415?casa_token=oyqqEGqc7LkAAAAA:R6F5BD6-9EluZp7TCIDKGMrXit_ifnrJ7UOprNbwOhPX0dY_7g1vbgC9uCYOuzu0scfVTQJkHJo) I think there should be (optional) MOI.Test tests for facial reduction certificates. @blegat what do you think?

chriscoey

Can also probably do it without needing values for both primal and dual variables Particular use case is when just changing the b-vector in a mixed integer convex OA algorithm....

chriscoey

With this PR, when the user uses the sampling basis, e.g. with ```julia @constraint(model, p in SOSCone(), zero_basis = BoxSampling(-ones(nvariables(p)), ones(nvariables(p)))) ``` the constraint will be transformed to `Hypatia.WSOSInterpNonnegativeCone` and...

blegat

...as the parameter was removed in #825

projekter