Solve BMI with CVX

Nonconvex
1

Can we solve the BMI :
P*P>=Q
with CVX?
Thanks

2

Is the BMI convex? Unless it is a “trivial” BMI which can be formulated as an LMI, it is not convex, and can not be handled directly by CVX.

If you can work out a bisection scheme or something in which CVX is called iteratively to solve a series of LMIs, or alternating fixing one BMI variable at a time,then you could use CVX to help solve a BMI, if your iterative scheme is successful.

However, what you have is not really a BMI.
Presuming Q is psd, reformulate it as an LMI:

Qchol = chol(Q);
[P Qchol; Qchol’ P] == semidefinite(2*size(Q,1))

I recommend you study “Convex Optimization”, by Boyd and Vandenberghe, freely available at http://stanford.edu/~boyd/cvxbook/ , to help you learn how to more effectively formulate LMIs. That will help you use CVX more effectively.

3

Many thanks Dear professor.

4

I’m not a professor. Just a humble Operations Research/Applied Math/System Analysis practitioner who happened to stumble across CVX.

5

Kind regards. Many thanks for your guidance.