This is my problem. R and W is variable. R is a scalar, W and Fk is a symmetric positive semidefinite matrix, To tackle the coupled variables R and W, I decide to use the bisection search method to solve the problem. Specifically, I will replace R in problem by a constant, and solve the resulting feasibility problem reduced from the problem. But I don’t know how to express the problem in CVX when the optimization objective is a constant.

Maybe you are not showing everything but this looks like all conditions here are linear so you have a straightforward SDP without the need to decouple anything.

A feasibility problem can be specified by not including minimize or maximize (objective), as shown below.
cvx_begin sdp
variable Theta(N_RIS,N_RIS) hermitian semidefinite;
subject to
for n = 1:N_RIS
Theta_W(n,n) == 1;
end
A feasibility problem can also be specified by including minimize 0, as shown below.
cvx_begin sdp
variable Theta(N_RIS,N_RIS) hermitian semidefinite;
minimize 0
subject to
for n = 1:N_RIS
Theta_W(n,n) == 1;
end

@wujunyi This is an English language forum. Please make any additional posts in English. Use Google translate or some other tool if you need to, perhaps with a disclaimer if you are not sure how good the translation is.

If you need to communicate with a poster using a language other than English, please use the forum Message capability, i.e., PM.