hello, i don’t know how to solve this problem using cvx,because there is as LMI as a constraint. Can you help me?
N = 10;
A = randn(10);
B = randn(10);
C = randn(10);
D = randn(10);
a = 0.5;
b= 5;
cvx_begin
variable w(N,1)
variable x
minimize (sum_square(w))
subject to
xeye(N)+Aw*w’*B == semidefinite(N);
cvx_end
Reformulate with Schur complement.
[a*eye(10) B*w;w'*B' 1]==semidefinite(11)
Your program is inconsistent with the image. I assume objective really is minimize (see below), otherwise this would be non-convex. And, as in the image, you need B and B’ in the semidefinite constraint, not A and B as in your program.
The image’s uses of H rather than T suggests w is intended to be complex. But I’ll let you fix up these details.
With the formulation as is, the solution is trivially all zeros for w. So perhaps the image is 'correct", and the objective is really to maximize. That would make the problem non-trivial, and also make it a non-convex nonlinear SDP for which CVX can’t be used.
thank you very much, i have got it.