Objective function bridge

[blegat]

It would be nice to have a bridge that transforms an unsupported objective into a SingleVariable objective with a LessThan (or GreaterThan depending on objective sense) constraint.
See jump-dev/SCS.jl#111 (comment)

[blegat]

It could also bridge SingleVariable to ScalarAffineFunction, it would resolve jump-dev/Cbc.jl#96

[rschwarz]

Nice, we have the same issue in SCIP.jl.

[blegat]

The short term solution is simply converting it to MOI.ScalarAffineFunction like what is done in jump-dev/SCS.jl#116. MOI.ObjectiveFunctionType is wrong though for SCS since it does not remember that it was set as MOI.SingleVariable but that is acceptable as a short term solution.

[arnavs]

I just wanted to follow up on this issue and see if there's been any movement. As it stands currently, my Mosek license is basically unusable in Julia, so it would be great to merge stuff even if it's a bit clunky.

[odow]

As it stands currently, my Mosek license is basically unusable in Julia

It looks like you successfully followed the instructions here jump-dev/MosekTools.jl#2?

so it would be great to merge stuff even if it's a bit clunky.

This isn't implemented yet. If you would like to have a go, we can point you in the right direction.

[arnavs]

Yeah, the issue with that workaround is that it only holds for problems with all positive eigenvalues, as @blegat points out.

Yeah, would be happy to. If you could briefly describe what needs to be done, I'll give it a shot.

[odow]

Yeah, the issue with that workaround is that it only holds for problems with all positive eigenvalues

Mosek is a convex solver. If the matrix isn't PSD (i.e., it has negative eigenvalues), Mosek can't solve it.

[arnavs]

Just to be clear, the problem we're discussing is a quadratic objective z' L z + z' q for some vectors z, q, and some matrix L, with (in my setup) zero or one negative eigenvalues.

I thought I was able to solve this problem before, but maybe we used different parameters. Maybe I was hallucinating.