How to solve LMIs with equality constraints using MATLAB?

Hi

I would like to find n by n matrices P and Q that minimize

*J = norm(P) + w*norm(Q), where w is a given weight,

subject to

P>=0, Q>=0, and f(P,Q)=0, where f(P,Q)=0 is a given function of P and Q.*

I tried to solve this problem using the lmi solver of MATLAB, but have no idea how to deal with the equality constraint: f(P,Q)=0.

f(P,Q)=0 is equivalent to f(P,Q)>=0 and f(P,Q)<=0, but MATLAB only solves strictly feasible constraints.

But the above problem contains not strictly feasible constraints.

Is there any good solution to handle this kind of problem using MATLAB?

Thank you.

[Torsten]

Why not using "fmincon" ?

Best wishes

Torsten.

[David Cho]

Torsten - Thank you for your comment.

How can we use 'fmincon' for multiple decision variables (P and Q)?

Also, in this problem the decision variables are matrices.

Answer 1

[Frank]

Section 2.5 of Byod's book Linear Matrix Inequalities in System and Control Theory specifically talks about this problem.