I have the following optimization problem.
\hspace{35pt}\max_{p_{n,k} w_{n,k}} t
subjected to
\hspace{35pt}t<= \sum_{n=1}^{{N_l}} w_{k,n} \log_2 \bigg(1 +\frac{p_{k,n} H_{k,n}} {w_{n,k} C}\bigg)
\hspace{35pt}p_{k,n}>=0
\hspace{35pt}w_{k,n}>=0
\hspace{35pt}sum(sum(p)) <= Pmax
\hspace{35pt}sum(w,2)<=1
p and w are my primal variables, rest are constants.
The term in the RHS of the constraint is concave as
\hspace{35pt}f = w \cdot \log_2(1+p/w)
is concave.
I am adding the 1st constraint in cvx in a loop
for k = 1:K
\hspace{35pt}t<= sum(
\hspace{35pt}w(:,k).*log(w(:,k).*c + p(:,k).*h(k)) -
\hspace{35pt}entr(w(:,k)) +
\hspace{35pt}(w(:,k).*log(c)))
end
But CVX is not allowing me to write this constraint. Can someone help me represent it in DCP complaint format?
