Exporting an SDP in an kernel representation

[Tomas Prijmeni]

Hello, is it possible to extract the kernel representation (primal) of an SDP problem in YALMIP?

I see there is an "export" function, but can't make heads or tails of the variables.

If I pass in the sdpsettings solver = sedumi, but I get the dual form instead.

As a proof of concept, it would really help if someone could show me on an example, where you

setup an sdp model; extract the variables; and pass them back in as a model in the kernel representation.

I'm imagining something vaguely like the following:

example_objective = ...

example_constraints = ...

[A, C, b] = export(example_objective, example_constraints)

X = sdpvar(...)

primal_objective = trace(C' * X)

primal_constraints = [X >= 0, trace(A(:,1)' * X) == b(:,1), ...]

optimize(primal_objective, primal_constraints)

The test in this case would obviously be, that the solution from the original model and the exported one should agree.

Is something like that possible? Thank you very much!

[Johan Löfberg]

You will have to apply dualization

https://yalmip.github.io/tutorial/automaticdualization/

[Tomas Prijmeni]

Aha! And that will change the output variables from the "export" function?

Great, thanks, I'll try that! :)

(Also, BTW, wow you are fast with your responses!)