How can I express this constraint?

1

How can I express this constraint? The yellow marks are my optimization variables, which are the matrices of 1k, kk, kk respectively, and the denominators hi and hij are the matrices of 1k and kk respectively. Similarly, l_ij is also kk matrix. I have written the following code, but it seems to be expressed in a non-standard way. Because there is a sum for j, so I don’t know how to express it.

1705478787637
17054787876371079×122 15.2 KB

subject to
        for i = 1:Device_num
            (exp(inv_pos(Power_s(i)) * log(2)) - 1) * l_s(i) / H_i(i) +...
                +sum((exp(inv_pos(Power_ijD(i,:)) * log(2) ) - 1) * l_d(i,:) / H_ij(i,:)) +...
                + sum ((exp(inv_pos(Power_ijr(i,:)) * log(2) ) - 1) * l_r(i,:) / H_i(i)) <= p / (Band * N0);
        end
        Power_s >= 0
        Power_ijD >= 0
        Power_ijr >= 0
cvx_end
2

This general idea should work. You can adapt to handle your actual situation, including dependence on i…

a=[1;2;3;4];
cvx_begin
variable x(4)
(2.^inv_pos(x)-1).*a, sum((2.^inv_pos(x)-1).*a)

ans =
cvx log-convex expression (4x1 vector)
ans =
cvx log-convex expression (scalar)