How to solve generalized SDP in cvxopt?

[kko]

Hi,

I want to solve the following optimization problem.

The hard constraint can be written as an LMI in in $P_{i,j}$. Semidefine program (SDP) also have LMI constraint but with linear objective in $P_{i,j}$. So, this problem can be considered as a generalization of SDP.

I have checked documentation of CVXOPT, but could not find a solver specifically for this. I believe there should be a solver for this problem as it is a well known problem especially in control community. Can anyone point me a solver for this? 

Thanks. 

[Martin]

You can use cvxopt.solvers.cp:

http://cvxopt.org/userguide/solvers.html#nonlinear-convex-optimization