Is MSK_toconic available in the Julia API?

[mtanneau]

I cannot find the MSK_toconic function (which is part of the C API) in the Julia wrapper.
Is it possible to add it to this API?

I am trying to compare various approaches for solving MIQPs/MIQCQPs with MOSEK. I'm trying to access to the conic reformulation computed by MOSEK for fair comparison.

[erling-d-andersen]

I do not understand the motivation. MOSEK can solve MIQP and MIQCQP directly and that is what a normal users would do.
So why do you need a conic reformulation.

[mtanneau]

I am comparing different approaches & formulations for solving MIQPs.
According to the MOSEK documentation, MIQPs are converted to conic form before being solved.

For instance, 1/2 x'Qx can be formulated as (1, r, Fx) ∈ Qr^{n+2} if Q = F'F.
Obviously, I can do such a reformulation manually, I just want to ensure that I get the same conic form as MOSEK's internal reformulation.

[erling-d-andersen]

If you feed the MIQCQP in something close MSK_toconic will be called internally. If you should do something differently you should rewrite the problem by hand. That means you can be more clever than Mosek can i.e. exploit the ideas outlined in

https://docs.mosek.com/whitepapers/qmodel.pdf

for instance.

I would myself always formulate directly on conic form to obtain the best results rather than relying on some automatic procedure. An automatic produce will never be as good as what a good human can do.

Btw I am not even sure the MSK_toconic could work in a Julia context. Since normally you feed in a problem and can then ask for solution. Here you ask for a transformation of one problem to another. It might be possible but most likely require quite some work.

[erling-d-andersen]

No point in keeping this open.