You haven’t show a complete program, with all variable declarations. Nor do I know what values the input data has Nor how your program supposedly corresponds to the problem definition shown in the image…
Nevertheless, based on the error message, it appears that Rlb_n_i(i) and hence sum_Rlb_n_i(i) are convex due to abs(P(n) - Pl(n))). The error message then occurs because convex >= constant is a non-convex constraint. Note that concave >= constant and ``convex <= constant` are convex constraints.
Whether the non-convex constraint in your code is really supposed to be the constraint is for you to determine, since I don’t understand what your problem actually is.given the hodgepodge of symbols with no clear definition as to which are optimization variables, and what any unstated relations may be.
Thanks for your reply.
The overall code for my question is as follows：
Pl = p_N_t;
l = 0;
sum_except_i = sum(H_N_Kb_all(n, .* (l_N_k .*Pl(n))) - H_N_Kb_all(n, i) * Pl(n) * l_N_k(i);
A_Pl = (log(1 + (H_N_Kb_all(n, i) * Pl(n) * l_N_k(i)) )/ log(2) )./ (N_noise + sum_except_i);
B_pl = (H_N_Kb_all(n, i) * l_N_k(i)) ./ (log(2) * (H_N_Kb_all(n, i) * Pl(n) * l_N_k(i) + N_noise + sum_except_i));
cvx_clear
cvx_quiet(true)
cvx_begin
variables P(N_bs, 1)
expression sum_Rlb_n_i(k_all)
minimize (sum(-log(P) / log(10)))
subject to:
for n = 1:N_bs
sum_Rlb_n_i(i) = 0;
for i = 1:k_all
Rlb_n_i = l_N_k(i)*W_bs_RB(n) * (A_Pl + B_pl * abs(P(n) - Pl(n)));
sum_Rlb_n_i(i) = sum_Rlb_n_i(i) + A_N_K_up_low(n, i) * Rlb_n_i;
end
sum_Rlb_n_i(i) >= R_sum_min ;
end
In these codes:
The dimension of matrix (HN_Kb_all) is (N_bs, k_all)；The dimension of matrix (l_N_k) is (1, k_all)；The dimension of matrix ( p_N_t) is (N_bs, 1).
The definitions of some constants in the code are:
N_bs=4;k_all = 100;K_b=25;
Based on your previous reply, I need to set the constraint (sum_Rlb_n_i (i)>=R_ Sum_ Rewrite as “concave>=constant” or “convex<=constant” constraint. So I can change this constraint to a convex constraint?
Looking forward to your reply.
concave>=constant” or “convex<=constant” would be accepted by CVX, but they are NOT equivalent to your code. I.e., sum_Rlb_n_i(i) <= R_sum_min would be accepted by CVX, but it is a different model. You have to determine what model is correct for the phenomenon you are modeling.
If your problem really is non-convex, you might want to consider using YALMIP with a non-convex solver.
Thank you for your suggestion. I adopted your suggestion to rewrite the constraint to (concave>=constant), and the convex optimization problem was successfully solved.
.* (l_N_k .*Pl(n))) - H_N_Kb_all(n, i) * Pl(n) * l_N_k(i);