What to do about this： Invalid constraint: {real constant} <= {invalid}

chaochaoliu235 · April 1, 2024, 10:05am

This is my code:
clear all
c0 = 0.6; % 环境常数
d0 = 0.11; % 环境常数canhu
LoS = 1; % Line-of-Sight (LoS) 路径损耗
NLoS = 20; % Non-Line-of-Sight (NLoS) 路径损耗
hmin = 199; % UAV的最小高度
L = 1000; % 远程基站的位置
N = 3; % 接入点的数量
APs = [-84.5, -21.6, 0; 250.3, 5.9, 0; -331.5, 62.7, 0]; % 接入点的坐标
UAV = [0, 0, 0]; % UAV 的坐标
dud = [L, 0, 0]; % UAV到远程基站的距离
Pmax = 1; % 最大发射功率
Bt = 1; % 总可用带宽
N_0 = 1e-15; % 噪声功率谱密度
P_s=1;%固定值
beta1 = 0.5; % 接入链路带宽分配系数固定值
beta2 = 0.5; % 回传链路带宽分配系数固定值
P_u=1;%P_u=Pmax

% 给定的参数
rho0 = -80;
Omega_NLoS = 20;
Omega_LoS = 1;

% 计算A和B
A = rho0 * 10^(-0.1 * Omega_NLoS);
B = rho0 * (10^(-0.1 * Omega_LoS) - 10^(-0.1 * Omega_NLoS));

% 计算每个远程基站到 UAV 的距离
dm1 = norm(UAV - APs(1, :));
dm2 = norm(UAV - APs(2, :));
dm3 = norm(UAV - APs(3, :));
dm4 = L; %1000

%迭代
alpha_var1_l=0.3;alpha_var2_l=0.24;alpha_var3_l=0.31;alpha_var4_l=0.117;
t_l=0.132;
h_u_l=82;
tau_var1_l=14.2;tau_var2_l=0.181;tau_var3_l=0.10;

cvx_begin
variables theta ;
expressions alpha_var(4) tau_var(3) s(4) pi_var h_u t ;
maximize(pi_var)
subject to
tau_var(1)=1.8; tau_var(2)=2.4; tau_var(3)=3.9;
alpha_var(1)=1.1; alpha_var(2)=2.1; alpha_var(3)=3.3; alpha_var(4)=4.5;
s(1)=1.5; s(2)=48; s(3)=3; s(4)=0.7;
h_u=100;t=24;pi_var=7;
h_u >= hmin; % Constraint (6g) ok
pi_var <= Ntheta; % Constraint (8c) ok
%pi_var <= Btbeta2log2(1 + (P_u * alpha_var(4)) / (Btbeta2N_0)); % Constraint (14c) ok
pi_var <= Btbeta2*-rel_entr(1,1 + (P_u * alpha_var(4)) / (Btbeta2N_0)) / log(2); % Constraint (14c) ok
inv_pos(t) <= h_u; % Constraint (18) ok

    % Constraint (28c)ok
    %(D_su.^2)./(A + B*c0.*(s_s_u - 15).^d0) <= f_alpha_su
    (dm1^2+h_u^2)*inv_pos(A + B*c0*pow_p((s(1) - 15),d0)) <= (2/alpha_var1_l-alpha_var(1)/alpha_var1_l^2);%分分开写/注意分母alpha_var应该有l
    (dm2^2+h_u^2)*inv_pos(A + B*c0*pow_p((s(2) - 15),d0)) <= (2/alpha_var2_l-alpha_var(2)/alpha_var2_l^2);
    (dm3^2+h_u^2)*inv_pos(A + B*c0*pow_p((s(3) - 15),d0)) <= (2/alpha_var3_l-alpha_var(3)/alpha_var3_l^2);
   
    % Constraint (28d)OK
    15 <= s(1) ; s(1) <= (180*inv_pos(pi_var))*atan(1*inv_pos(dm1*t));
    15 <= s(2) ; s(2) <= (180*inv_pos(pi_var))*atan(1*inv_pos(dm2*t));
    15 <= s(3) ; s(3) <= (180*inv_pos(pi_var))*atan(1*inv_pos(dm3*t));
  
    % Constraint (28e)ok
    (L^2+h_u^2)*inv_pos(A + B*c0*pow_p((s(4) - 15),d0)) <= (2/alpha_var4_l-alpha_var(4)/alpha_var4_l^2);
    
    % Constraint (28f)ok
    15 <= s(4) ;  s(4) <= (180*inv_pos(pi_var))*(atan(1*inv_pos(L*t)));
    
    % Constraint (28g) 注意i=2...N
  
    % log(tau_var(1)) + log(dm1^2+1/(t_l)^2)-(2*(t-t_l))/(dm1^2*(t_l)^3+t_l) >= ...
    %     log(A+B*c0*((180/pi_var)*atan(h_u_l/dm1) - 15)^d0) + (h_u-h_u_l) * (((180/pi_var)*B*c0*d0*((180/pi_var)*atan(h_u_l/dm1)-15)^(d0-1)*(dm1/(dm1^2+h_u_l^2))) ...
    %         /(A+B*c0*((180/pi_var)*atan(h_u_l/dm1)-15)^d0));  

   real(-rel_entr(1,tau_var(2)) + -rel_entr(1,dm2^2+inv_pos((t_l)^2))-(2*(t-t_l))/(dm2^2*(t_l)^3+t_l))  <= ...
         -rel_entr(1,A+B*c0*pow_p((180*inv_pos(pi_var)*atan(h_u_l/dm2) - 15),d0)) + (h_u-h_u_l) * ((180*inv_pos(pi_var))*B*c0*d0*pow_p(((180*inv_pos(pi_var))*atan(h_u/dm2)-15),(d0-1))*(dm2/(dm2^2+h_u_l^2))) ...
           /(A+B*c0*((180*inv_pos(pi_var))*atan(h_u/dm2)-15)^d0) ;

    -rel_entr(1,tau_var(3)) + -rel_entr(1,dm3^2+1/(t_l)^2)-(2*(t-t_l))/(dm3^2*(t_l)^3+t_l) <= ...
         -rel_entr(1,A+B*c0*pow_p((180*inv_pos(pi_var)*atan(h_u_l/dm3) - 15),d0)) + (h_u-h_u_l) * ((180*inv_pos(pi_var))*B*c0*d0*pow_p(((180*inv_pos(pi_var))*atan(h_u/dm3)-15),(d0-1))*(dm3/(dm3^2+h_u_l^2))) ...
           /(A+B*c0*((180*inv_pos(pi_var))*atan(h_u_l/dm3)-15)^d0) ;

    % Constraint (28h)
    theta <= Bt*beta1*-rel_entr(1,sum(P_s*alpha_var(1)+P_s*alpha_var(2)+P_s*alpha_var(3))+Bt*beta1*N_0)/log(2)-Bt*beta1 ...
        * -rel_entr(1,sum(P_s*tau_var2_l+P_s*tau_var3_l)+Bt*beta1*N_0)/log(2)+(1/log(2))*(sum(P_s*(tau_var(2)-tau_var2_l)+P_s*(tau_var(3)-tau_var3_l))) ...
          /(sum(P_s*tau_var(2)+P_s*tau_var(3))+Bt*beta1*N_0) ; %i=1
      
    theta <= Bt*beta1*-rel_entr(1,sum(P_s*alpha_var(2)+P_s*alpha_var(3))+Bt*beta1*N_0)/log(2)-Bt*beta1 ...
        * -rel_entr(1,sum(P_s*tau_var3_l)+Bt*beta1*N_0)/log(2)+(1/log(2))*(sum(P_s*(tau_var(3)-tau_var3_l))) ...
          /(sum(P_s*tau_var(3))+Bt*beta1*N_0) ; %i=2
    
    theta <= Bt*beta1*-rel_entr(1,sum(P_s*alpha_var(3))+Bt*beta1*N_0)/log(2)-Bt*beta1 ...
        * -rel_entr(1,Bt*beta1*N_0)/log(2)+(1/log(2))* 0; %i=3

cvx_end
The result of the run is：

How do I change my code to deal with this error？Looking forward to your answers.

Mark_L_Stone · April 1, 2024, 11:00am

{invalid} usually means that one or more of the input data is NaN, which CVX considers to be invalid. Sometimes this happens when the optimal variable value of a previous CVX problem is used as the input to the current CVX problem, but that previous problem was not solved to (finite) optimality, and CVX populated the variable values with NaN.

it may also be that “extreme” input data such as N_0 being 1e-15 might cause numerical difficulties and failure for the solver, but should not result in the {invalid} error message in the current CVX problem, although if optimal variable values are used in a subsequent problem, could cause the error message in that subsequent problem.

chaochaoliu235 · April 1, 2024, 2:29pm

Thank you for answering my question in your busy schedule, thanks!