I have a less-than inequality constraint,where I2 is the left side,the right side is a constant.
How to express I2?and the yellow letter(y) is variable, y(2,1).
How to express this function in CVX?
(25) looks doable. (26) does not look convex, per my interpretation.
You ought to be able to handle the LHS (i.e., (25)) using the first approach in section 5.2.7 Log-sum-inv of https://docs.mosek.com/modeling-cookbook/expo.html#exponential-cone by using CVX’s log_sum_exp for the ti >= … constraint, and also include the xi >= … constraint in that link as written.
x1 would be 1/rho, and the other xi’s would be something like (H^2+sk)/(beta1*pk) with indices suitably fixed up. And multiply the RHS by log(2) to account for log2.
Constraint (26) does NOT look convex to me. So I don’t see what the authors of that book or paper were doing.
Thank you for your attention, I have not done this paper yet. You can reference these code, I hope it can help you.
for i=1:N
v(n)=inv_pos( (H2+s(n))/(beta*p(n)) ); %calculat fraction v
end
for i=1:N
V(i)=sum(v([1:i-1 i+1:N]))+rol; % sum+rol
end
for i=1:N
I2(i)=I2_f(i)+I2_df(i)*(V(i)-V_f(i)); % Taylor
end
% I2_f(i)--- the feasible value of I2
% V_f(i)---the feasible value of V, V=sum+rol
% I2_df(i)---the feasible value of 【derivative of log(V) in term of V】