CVX： Ineffectiveness of restraints!

[Dxy0529]

clc
c
clear
beta_0 = 10^-9 ;
ka = 4;
Ka = 3;
numUsers = 20; %number of users
numSubband_all = 5:5; %16;
npsd = -174; %noise power spectral density dBm/Hz
W = 10^6; %subband bandwidth 1MHz
%数量级增大 很关键 ！！！！！！！！
noise_power = 10^(-14.4) * 10e13;
Q_b = [1500,1500];
v = 15;
T_opt = zeros(1,length(numSubband_all));
H1 = 100ones(numUsers,1); %无人机高度
H = 100;
for i = 1:length(numSubband_all)
numSubband = numSubband_all(i); %number of subband
R = 250;
theta=0:2pi/1000:2pi;
a=Rcos(theta);
b=Rsin(theta);
%---------------------蜂窝用户----------------------------
t1=rand(1,numUsers);
t2=rand(1,numUsers);
for i1=1:numUsers
beta(i1)=2pit1(i1);
r(i1)=2Rt2(i1)-R;
user_x(i1)=r(i1)cos(beta(i1));
user_y(i1)=r(i1)sin(beta(i1));
end
ruser = [user_x’,user_y’];
R_s = randi([10^6,10^7],numUsers,1);
Pow = unifrnd(0.1, 0.2, numUsers, 1);
d_bar = randi([10^9,10^10]);
%初始点设置
t3=rand(1,1);
t4=rand(1,1);
for i1=1:1
beta1(i1)=2pit3(i1);
r(i1)=2Rt4(i1)-R;
uav_x(i1)=r(i1)cos(beta1(i1));
uav_y(i1)=r(i1)sin(beta1(i1));
end
Quav = [uav_x,uav_y];
objection_0 = 0;
jj =1;
iteration =1;
max_iterations =10;
while 1
d = pdist2(ruser, Quav, ‘euclidean’);
d = d+ H1.^2;
beta = sqrt(beta_0 * 1e28) ./ d ; % 大尺度
g_rayleigh = sqrt(0.5) * (randn(numUsers, numSubband) + 1i * randn(numUsers, numSubband));
g_rician = sqrt(Ka/(Ka+1)) + sqrt(1/(Ka+1)) * g_rayleigh;
%为了消除虚数
g_rician_dB = 20 * log10(abs(g_rician));
g_rician = 10 .^ (g_rician_dB / 10);
for i3 = 1:numSubband
g(:,i3) = g_rician(:,i3) . beta ;
end
%transmission data rates of different users with different subbands
R_t = Wlog2(1+Powones(1,numSubband).g/noise_power) ;
e_all = (1./(R_sones(1,numSubband)) + 1./( R_t)) ;
[Assigned_subband_index,cost] = assignmentoptimal(- e_all.^-1);%should maximize the sum of the weight, while the function is minimization!!!
Scheduled_user_index = find(Assigned_subband_index~=0);
Alpha_of_ScheUser = e_all(sub2ind(size(e_all),find(Assigned_subband_index~=0), Assigned_subband_index(Assigned_subband_index~=0)));
d_opt = ( ( d_bar)./Alpha_of_ScheUser/(sum(Alpha_of_ScheUser.^(-1))));
len1 = length(Scheduled_user_index);
cvx_begin
%cvx_solver mosek
cvx_solver sedumi
variable Q(1,2)
variable mu1 nonnegative
variable gamma1(1,len1) nonnegative
expression R_LB(1,len1)
for k = 1:len1
index = Scheduled_user_index(k);
index_subband = Assigned_subband_index(Scheduled_user_index(k));
%计算信道增益
g_c = g_rician(index,index_subband);
ita = Pow(index)* g_c sqrt(beta_0 1e28) /noise_power;
R_LB(k) = ( W*(-rel_entr(1,(1+ita/ ( (pow_pos(norm((Quav-ruser(index,:)),2),2)+H^2))))/log(2)) + ita * W * (-1)(pow_pos(norm((ruser(index,:)-Q),2),2)-pow_pos(norm((Quav-ruser(index,:)),2),2)) /(((pow_pos(norm((Quav-ruser(index,:)),2),2)+H^2) +ita) (pow_pos(norm((ruser(index,:)-Quav),2),2)+H^2) log(2)) );
end
Q_d = [Q - Q_b, H];
Tround = norm(Q_d) /v;
objection = mu1 + 2Tround ;
minimize objection
subject to
for k= 1:len1
R_LB(k) >= gamma1(k) ;
end
for k = 1: len1
d_opt(k) / (R_s(Scheduled_user_index(k))) + d_opt(k) * inv_pos( gamma1(k) ) <= mu1;
end
abs( Q(1,1))<= 250 ;
abs( Q(1,2))<= 250 ;
cvx_end
disp(Q)
disp(mu1)
disp(Tround)
jj=jj+1;
if abs(objection - objection_0) <= 1e-4
T(iteration) = objection;
iteration = iteration +1;
break;
else
Quav = Q;
objection_0 = objection;
T(iteration) = objection;
iteration = iteration +1;
end
end
Q
objection
iteration
end
T
figure
plot(1:iteration-1,T)

Calling SeDuMi 1.3.4: 81 variables, 36 equality constraints
For improved efficiency, SeDuMi is solving the dual problem.

SeDuMi 1.3.4 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 36, order n = 65, dim = 82, blocks = 17
nnz(A) = 119 + 0, nnz(ADA) = 196, nnz(L) = 123
it : by gap delta rate t/tP t/tD* feas cg cg prec
0 : 1.90E+06 0.000
1 : -8.65E+04 5.04E+05 0.000 0.2649 0.9000 0.9000 1.90 1 1 1.9E+00
2 : -5.64E+04 1.30E+05 0.000 0.2586 0.9000 0.9000 1.84 1 1 6.7E-01
3 : -8.74E+03 4.14E+04 0.000 0.3175 0.9000 0.9000 1.64 1 1 3.9E-01
4 : -1.69E+03 1.25E+04 0.000 0.3013 0.9000 0.9000 1.35 1 1 3.0E-01
5 : -7.02E+02 4.01E+03 0.000 0.3211 0.9000 0.9000 1.14 1 1 2.8E-01
6 : -2.14E+02 1.28E+03 0.000 0.3185 0.9000 0.9000 1.14 1 1 2.6E-01
7 : -2.20E+02 4.75E+02 0.000 0.3723 0.9000 0.9000 1.17 1 1 2.6E-01
8 : -2.50E+02 1.54E+02 0.000 0.3250 0.9000 0.9000 1.18 1 1 3.7E-01
9 : -2.50E+02 5.26E+01 0.000 0.3408 0.9000 0.9000 1.11 1 1 1.1E-01
10 : -2.39E+02 1.52E+01 0.000 0.2896 0.9000 0.9000 1.08 1 1 3.1E-02
11 : -2.36E+02 4.14E+00 0.000 0.2715 0.9000 0.9000 1.20 1 1 6.6E-03
12 : -2.36E+02 3.01E-01 0.000 0.0727 0.9900 0.9900 1.32 1 1 3.2E-04
13 : -2.36E+02 1.88E-03 0.000 0.0062 0.9990 0.9990 1.07 1 2 1.9E-06
14 : -2.36E+02 4.43E-04 0.000 0.2359 0.9000 0.9000 0.99 4 4 4.4E-07
15 : -2.36E+02 2.06E-05 0.000 0.0465 0.9900 0.9900 0.96 4 5 2.2E-08
16 : -2.36E+02 8.47E-06 0.000 0.4116 0.9046 0.9000 0.54 19 19 1.5E-08
17 : -2.36E+02 2.87E-06 0.396 0.3388 0.9000 0.0000 0.37 25 23 8.4E-09

iter seconds digits cx by
17 0.1 7.3 -2.3607907146e+02 -2.3607908303e+02
|Ax-b| = 6.7e-12, [Ay-c]_+ = 2.6E-06, |x|= 4.4e+00, |y|= 2.0e+06

Detailed timing (sec)
Pre IPM Post
1.300E-02 6.200E-02 3.007E-03
Max-norms: ||b||=1, ||c|| = 3.241228e+06,
Cholesky |add|=6, |skip| = 0, ||L.L|| = 713.195.

Status: Solved
Optimal value (cvx_optval): +236.079

250.0000 250.0000

-1.9856e-06

118.0395

The code can run, But clearly the constraints were ignored ”d_opt(k) / (R_s(Scheduled_user_index(k))) + d_opt(k) * inv_pos( gamma1(k) ) <= mu1;“ Can you help me solve it please?

[Mark_L_Stone]

The solvers ensure constraints are satisfied to within a feasibility tolerance, which might be about 1e-6 or 1e-8. if constraints are violated by no more than that, the solver, and hence, CVX, consider the constraints to be satisfied.

[Dxy0529]

I tried to change the precision of some values like d_opt, the constraints work but the problem doesn’t converge, can you give me advice
?

[Mark_L_Stone]

The result obtained using the SeDuMi solver is inaccurate. The optimal solution is not as good as before the optimization.

Unsafeguarded (no line search or trust region)Successive Convex Approximation (SCA) or generally, alternating variables optimization are unreliable. It might not descend (for minimization problem), i.e., iterates could get worse. It might not converge to anything; and if it does converge, it might not be to a local optimum of the original problem, let alone a global optimum. The solution of successive iterations, and therefore subproblem inputs, can become wilder and wilder, until at some point …