I am trying to use SDP in CVX to solve the above problem. I have reformulated using LMI. I am given that a1 >= a2 >=1.
variables x1 x2 y z
minimize( x1+x2 )
But it is infeasible. Can you please help me to find a way to solve this problem? if I do [y z; z 1]>=0, then I think I change the constraint.