How to use CVX to solve feasibility problem?

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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.

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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.

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

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

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Of course. I missed one of the R

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Ok, thank you very much for your reply！

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Thanks for your reply!

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@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！！！

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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

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@ccsnow
您好，您这个是上面非凸问题全部代码吗，这里面的目标函数以及二分搜索法在哪里体现呢？约束前两个在哪里体现呢？

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

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@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.

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ok.I’ll pay attention