The cvx solves convex problems but inequality constraints sometimes take equal sign and sometimes not

When solving the above problem with cvx, the C7~C9 constraint should take equal sign or approximate equal sign, but sometimes it is not normal. After all, the right side of the inequality is the increasing function of E.V>0,v>0.

How big is the gap you got when it turned out not equal? It is normal if the gap is small. If its not, it could be some of your input data are too small (like 10^(-12)) or too big (10^(12)) or something else. Please show all your CVX and solver output, and, maybe provide a runnable code in Markdown format for the expert to reproduce.

Yes, not only is it unequal and sometimes the gap is huge.

For E, there is no large or small input, such as the order of V is usually on the order of 10 ^ -3, and the order of X (k) is usually on 10 ^ -4.

The signal to noise ratio in Shannon’s formula is usually between 10 ^ 3 and 10 ^ 6.

So it is very strange to get a solved E, which is much larger.

The state of each solution is “solved”.