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 R.
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?