Why does the optimal value become NaN sometimes?

1

Why does the optimal value become NaN sometimes? i had write the code as the paper shown

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My code

hat_p_lowr=0.0317;
%OP4
%declare
K=4;%K channel
N=4;%N  antenna
L=5;%distance between RX & TX
xi=10^-4%tolerence between 
nois_var_hk_2pow=0.1*(L^(-2.5));%W,0.1*(L^(-2.5)),if this unit is dbm
nois_var_ak_2pow=[1.0000e-10 1.0000e-10 1.0000e-10 1.0000e-10 ];
nois_var_dk_2pow=[1.0000e-08 1.0000e-08 1.0000e-08 1.0000e-08 ];
bar_r=[10 10 10 10];
P_T=10;
h_1=sqrt(nois_var_hk_2pow/2)*(randn(N,1)+1i*randn(N,1));
h_2=sqrt(nois_var_hk_2pow/2)*(randn(N,1)+1i*randn(N,1));
h_3=sqrt(nois_var_hk_2pow/2)*(randn(N,1)+1i*randn(N,1));
h_4=sqrt(nois_var_hk_2pow/2)*(randn(N,1)+1i*randn(N,1));
h_kk=cat(2,h_1 ,h_2 ,h_3, h_4)
 for n=1:4
    h_k{n}=h_kk(1:4 , n);
    n=n+1;
 end


cvx_begin

    variable FNNK_lowr(N,N,K) semidefinite; %c7
    variable rho_k_lowr(1,1,K) semidefinite;
%==========================
%combined lots of FNNK
Fkk_lowr=cat(2,FNNK_lowr);
    
    lowr=0
   for o_lowr=1:4
       Fk_lowr{o_lowr}=Fkk_lowr(1:4,o_lowr+3*lowr:4*o_lowr)
       lowr=lowr+1;
   end
   tr_ace_lowr=0
   for t=1:K
       tr_ace_lowr=tr_ace_lowr+trace(Fk_lowr{t})  
   end
%====================================    
%object function
    minimize( tr_ace_lowr )
%==================================== 
%Constraint 
subject to 
%c3
rho_k_lowr<=1;

%===================================================
%c5
       c5_left_hand_lowr = 0;
        for k = 1:K
            sum_5_lowr = 0;
            for j = 1:K
                if j ~= k  
                 sum_5_lowr = sum_5_lowr +  h_k{k}' * Fk_lowr{j} * h_k{k};
                end
            end      
            c5_left_hand_lowr = c5_left_hand_lowr - sum_5_lowr+ (h_k{k}' * Fk_lowr{k} * h_k{k}*inv_pos(bar_r(1)))
            c5_right_hand_lowr= nois_var_ak_2pow(1)+ ( nois_var_dk_2pow(1)*inv_pos(rho_k_lowr(k)) )
            real( c5_left_hand_lowr ) >=   c5_right_hand_lowr
        end
%===================================================   
%c10
    c10_left_hand_lowr = 0;
        for k = 1:K           
            sum_10_lowr = 0;
            for j = 1:K
                 sum_10_lowr= sum_10_lowr +  h_k{k}' * Fk_lowr{j} * h_k{k};
            end
            c10_left_hand_lowr = c10_left_hand_lowr + sum_10_lowr+nois_var_ak_2pow(1)
            c10_right_hand_lowr=hat_p_lowr*inv_pos(1-rho_k_lowr(k))  
           real(c10_left_hand_lowr)>=  c10_right_hand_lowr
        end     
cvx_end
2

Depending on the random numbers used for h_1, h_2, h_3, h_4, the problem may be either feasible or infeasible. If it is infeasible, the optimal value is NaN.

You should look at the status reported by CVX/. If the problem is infeasible, the final output from CVX is

Status: Infeasible
Optimal value (cvx_optval): +Inf

Maybe you should now concentrate on realistic inputs rather than random inputs, and see whether they result in feasible problems which are solved to optimality.

3

yes,you are right,the status is infeasible when the cvx_optval is +Inf
but the channel is a random,so i can’t just let the channel be a realistic (constant ) value.

By the way,no matter the status is Infeasible or feasible,the channel ,h1~h4, are all complex number,and i don’t think they are not something very different.

Also ,i found that if i change bar_r from 10 to 1010^-7,the status will become feasible everytime.But the bar_r should be 10 instead of 1010^-7.Because the bar_r is the SINR value ,and be written as 10 dB in the paper. The unit of all parameters are Watt,so i think i don’t need to change something about that 10dB