HELP! How to implement it? I want to let ta_3=0, when cvx variables q_f=0. (tp is propogation delay.)

MIDCP
1 
        cvx_begin 
        variables q_f(N,AP)
        expression ta_4(UE,AP)
        expression tbh1(UE,N)
        ta_3 = 0;
        for m = 1:UE
            for j = 1:N
                for k = 1:AP
                        if map_UE_AP(m,k)~=0 
                            ta_4(m,k) =  prob_f(j)*q_f(j,k)*B/r_AP_UE(k,m)+prob_f(j)*tp(m,k)*q_f(j,k)*inv_pos(q_f(j,k)+eps);
                        else
                            ta_4(m,k) = 0;
                        end
                end
                ta_3 = ta_3+max(ta_4(m,:));
            end 
        end
       tbh = map_UE_AP*q_f';
       tbh = max(1-tbh,0);
       Tbh = sum(tbh*prob_f)*pms.time;  
       tt = ta_3 + Tbh;
       q = sum(q_f,1);
       minimize(tt)
       subject to
       0<= q_f(:,:) <=1;
       0<= q(:) <=C(:);
       cvx_end
2

In order for this to make sense, I will presume that ta_3 is also declared an N by AP CVX variable, and the statement ta_3 = 0 needs to be removed from the program.

You will need to choose a tolerance, small_positive_number for what constitutes equaling zero.

Let M_upper be upper bound for ta_3, and M_lower be lower bound for ta_3. I presume that M_lower <= 0, else your condition could never be satisfied.

My formulation utilizes that 0 <= q_f <= 1. If that were not the case, modifications would be required.

q_f < small_positive_number → b = 0, which forces ta_3 = 0.
q_f >= small_positive_number allows b = 1, which doesn’t additionally constrain ta_3.

variable b(N,AP) binary
q_f - small_positive_number >= b-1
ta_3 <= M_upper*b
ta_3 >= M_lower*b
3

Thanks for your reply! I’ll have a try.