SDP with quadratic objective

[Shahar Kovalsky]

Hi,

Say I have a problem with quadratic objective and LMI constraints.

How does Yalmip employ the objective -- as an LMI or an SOC (I use Mosek)? Which is generally more efficient? 

Thanks,

Shahar.

[Johan Löfberg]

Quadratic objective in a general conic model has to be placed in the constraint in mosek. Since Mosek supports SOCPs, there is no reason to lift the SOCP to an SDP. If that was the case, it would signal a poor implementation of the SOCP code compared to the SDP code. Hopefully Erling agrees...

[Shahar Kovalsky]

So, just to be sure I understand correctly; In this case Yalmip will do the "right" thing and generate a second order cone constraint (corresponding to the objective epigraph)?

[Erling D. Andersen]

Anything that can be formulated using SOC should definitely NOT be cast using the semidefinite cone. That will lead to major inefficiencies.

[Johan Löfberg]

Yes.

[Shahar Kovalsky]

Okay, great. Thanks Johan and Erling!