就是P9 s.t.后面的这个式子，U是半正定矩阵并且是H阵,我是这样表示的,好像在cvx求解时并未生效.希望可以得到解答，拜托了
cvx_begin sdp
variable U(N+1,N+1) hermitian
variable deta(1,1);
maximize (real(deta-yta*(trace(U)-lamda)-trace(vv’(U-Ut))));
subject to
deta>=0;
real(trace(GU))<=PI;
real(U(N+1,N+1))==1;
% log(real(trace(GABU)))+log(real(trace(GIEU)))-log(real(trace(GIBUt)))-log(real(trace(GAEUt))) …
% -real(trace(inv_pos(real(trace(GIBUt)))GIB(U-Ut)))-real(trace(inv_pos(real(trace(GAEUt)))GAE(U-Ut)))-deta>=R;
% 这个带log的限制条件好像表示的不对？？？感觉没有起作用
log(real(trace(GABU)))+log(real(trace(GIEU)))-log(real(trace(GIBUt)))-log(real(trace(GAEUt))) …
-real(trace(inv_pos(real(trace(GIBUt)))GIB(U-Ut)))-real(trace(inv_pos(real(trace(GAE*Ut)))GAE(U-Ut)))-deta>=R;
U == hermitian_semidefinite(N+1);
cvx_end
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Google translate says:
It’s the formula behind P9 s.t., U is a positive semidefinite matrix and it’s an H matrix, I’m expressing it, but it doesn’t seem to take effect when solving cvx. I hope you can get the answer, please
I don’t know what you mean by " it doesn’t seem to take effect ". Nevertheless, I don’t know what the specification of the optimization problem is, I don’t understand the conventions, assumptions, notation, what’s complex as opposed to real, etc… Perhaps U is supposed to be hermitian semidefinite, but I don’t see that specified in the image. If U is also supposed to be an H matrix, I don’t know what than means, because H matrix doesn’t have a unique standardized meaning H-matrix - Wikipedia .
I have no idea what the 2nd box is supposed to show. Are all the terms with the ln actually in the problem (if so, the >= is going the wrong direction to be convex), or is that some majorization to use the top or bottom lines instead of all the ln terms.
U^{(t)} looks suspiciously like it is part of Successive Convex Approximation (SCA), in which case the overall algorithm might be unstable and unreliable, even if you correctly enter each convex optimization subproblem.