# How to use CVX to solve feasibility problem?

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.

In my opinion, the constraint of (9b) is non-convex because of the coupled variables R and W.

A feasibility problem can be specified by not including minimize or maximize (objective).

Of course. I missed one of the R

@ccsnow 您好，打扰您一下，我也遇到您这种类似的可行性问题，可以分享一下这部分的代码吗，十分感谢！！！

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

@ccsnow

No, this is not complete code, I just want to show how to express the feasibility problem.

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ok.I’ll pay attention

Hi Mark, could you please consider the question in this post, it is also about feasibility problems:

Hi Michal, could you please consider the question in this post, it is also about feasibility problems: