Dear All, I have the following matrix structure for my problem:
variable W1(6,6) hermitian semidefinite variable W2(6,6) hermitian semidefinite variable W3(6,6) hermitian semidefinite W = [ W1(1:3,1:3) W1(1:3,4:6) oo oo W1(4:6,1:3) W1(4:6,4:6) W2(1:3,4:6) oo oo W2(4:6,1:3) W2(4:6,4:6) W3(1:3,4:6) oo oo W3(4:6,1:3) W3(4:6,4:6) ]; minimize (real(trace(A*W)) + real(trace(B*W)) + real(trace(C*W)) ) subject to W1(4:6,4:6) == W2(1:3,1:3); W2(4:6,4:6) == W3(1:3,1:3); W1 >= 0; W2 >= 0; W3 >= 0;
My question is if I want to construct the W1, W2 and W3 matrixes by using smaller Wij matrixes and each Wij is 3 by 3 matrix and rank-1 matrix.
How can I do that and what constraints should I put on my new Wij matrixes?
Thanks in advance for any help.