Hi,
I have difficulty in running the below op problem, which is a SCA.
%% main
clc
clear all
close all
cvx_solver sedumi;
para = para_init();
% Generates the channel vector
g1=compute_h(para.pathloss,8,para.theta1DL); % Channel of downlink user 1
g2=compute_h(para.pathloss,8,para.theta2DL); % Channel of downlink user 2
h1=compute_h(para.pathloss,8,para.theta1UL); % Indicates the channel of upstream user 1
h2=compute_h(para.pathloss,8,para.theta2UL); % Indicates the channel of upstream user 2
% Guide vector ar(theta0)
ar=compute_a(0,8);
% Generates the guidance vector covariance matrix
A0=compute_a(0,8)*compute_a(0,8)'; %A(theta0)
A1=compute_a(-50*pi/180,8)*compute_a(-50*pi/180,8)'; %A(theta1)
A2=compute_a(20*pi/180,8)*compute_a(20*pi/180,8)'; %A(theta2)
[Pmin,V0,V1,V2,pk1,pk2] = SCA_algorithm_1(para,g1,g2,h1,h2,ar,A0,A1,A2);
function [values] = para_init()
values.noise = 10^(-70/10); % Noise power -70dbm
values.K=2; % Upstream Users
values.L=2; % Downlink users
values.Nt=8; % Number of transmitting antennas
values.Nr=8; % Number of receiving antennas
values.Pmax=10^(48/10); % Maximum transmit power of the base station, w converted to mw multiplied by 1000
values.Pt=10^(35/10); % Maximum transmit power of the user
values.pathloss=10^(-103.6/10); % path loss
values.theta1UL=45*pi/180;
values.theta2UL=-75*pi/180; % Uplink user Angle
values.theta1DL=-40*pi/180;
values.theta2DL=60*pi/180; % Downlink user Angle
values.beita0=sqrt(10^(-10));
values.beita1=sqrt(10^(-5));
values.beita2=sqrt(10^(-5));
values.alpha=10^(-110/10); % Residual SI channel power -110dB
values.taoCOMDL=10^(12/10); % Downstream user SNR limit Ļ
values.taoCOMUL=10^(10/10); % Upstream user SNR limit Ļ
values.taorad=10^(15/10); % Radar SNR limit
end
%% SCA
function [Pmin,V0,V1,V2,pk1,pk2] = SCA_algorithm_1(para,g1,g2,h1,h2,ar,A0,A1,A2)
% initiate V0,V1,V2,Pk1,pk2
diagonal = rand(8, 1);
upperTriangular = triu(rand(8), 1);
A = diag(diagonal) + upperTriangular + upperTriangular';
V0=A;V1=A;V2=A;pk1=100;pk2=100;
Convergence = 0;
Pmin_old = inf;
while Convergence == 0
[Pmin, V0, V1, V2, pk1, pk2, cvx_status] = SCA_step(para,g1,g2,h1,h2,ar,A0,A1,A2,V0,V1,V2,pk1,pk2);
if strcmp(cvx_status, 'Infeasible')
V0=eye(8);V1=eye(8);V2=eye(8);pk1=1;pk2=1;
end
if (abs(Pmin_old - Pmin)< 100)
Convergence = 1;
break;
else
Pmin_old = Pmin;
end
end
end
%% SCA_step
function [Pmin,V0,V1,V2,pk1,pk2,cvx_status] = SCA_step(para,g1,g2,h1,h2,ar,A0,A1,A2,V0_pre,V1_pre,V2_pre,pk1_pre,pk2_pre)
cvx_begin
variable V0(8,8) complex semidefinite;
variable V1(8,8) complex semidefinite;
variable V2(8,8) complex semidefinite;
variable pk1;
variable pk2;
V0 == hermitian_semidefinite(8);
V1 == hermitian_semidefinite(8);
V2 == hermitian_semidefinite(8);
pk1>=0;
pk2>=0;
%some auxiliary
Q=V0+V1+V2;
Q_pre=V0_pre+V1_pre+V2_pre;
B=sqrt(para.beita1^2)*A1+sqrt(para.beita2^2)*A2+compute_HSI(8,8);
C=sqrt(para.beita0^2)*A0+B;
F=pk1*(h1*h1')+pk2*(h2*h2')+B*Q*B'+para.noise*eye(8);
F_pre=pk1_pre*(h1*h1')+pk2_pre*(h2*h2')+B*Q_pre*B'+para.noise*eye(8);
f1=pk2*(h2*h2')+C*Q*C'+para.noise*eye(8);
f2=pk1*(h1*h1')+C*Q*C'+para.noise*eye(8);
f1_pre=pk2_pre*(h2*h2')+C*Q_pre*C'+para.noise*eye(8);
f2_pre=pk1_pre*(h1*h1')+C*Q_pre*C'+para.noise*eye(8);
%target
f=trace(V0)+trace(V1)+trace(V2)+pk1+pk2;
minimize(f);
subject to
%constrain 20(c)
(1+1/para.taoCOMDL)*quad_form(g1,V1)>=quad_form(g1,Q)+para.noise;
(1+1/para.taoCOMDL)*quad_form(g2,V2)>=quad_form(g2,Q)+para.noise;
%constrain 20(a)which is 24
real(ar'*inv(F_pre)*ar-ar'*inv(F_pre)*(F-F_pre)*inv(F_pre)*ar)>=real(para.taorad/(para.beita0^2)*inv_pos(ar'*Q*ar));
%constrain 20(b)which is 26
real(h1'*inv(f1_pre)*h1-h1'*inv(f1_pre)*(f1-f1_pre)*inv(f1_pre)*h1)>=real(para.taoCOMUL*inv_pos(pk1));
real(h2'*inv(f2_pre)*h2-h2'*inv(f2_pre)*(f2-f2_pre)*inv(f2_pre)*h2)>=real(para.taoCOMUL*inv_pos(pk2));
cvx_end;
Pmin=f;
end
and the result is
Calling SeDuMi 1.3.4: 400 variables, 197 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 = 197, order n = 62, dim = 785, blocks = 10
nnz(A) = 1943 + 0, nnz(ADA) = 38809, nnz(L) = 19503
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 4.31E-01 0.000
1 : -4.39E+00 2.22E-01 0.000 0.5160 0.9000 0.9000 3.96 1 1 1.9E+00
2 : -1.60E+01 1.09E-01 0.000 0.4917 0.9000 0.9000 0.70 1 1 1.3E+00
3 : -2.41E+01 4.38E-02 0.000 0.4004 0.9000 0.9000 0.63 1 1 6.6E-01
4 : -3.32E+01 2.18E-02 0.000 0.4976 0.9000 0.9000 0.24 1 1 4.7E-01
5 : -4.62E+01 8.86E-03 0.000 0.4069 0.9000 0.9000 0.14 1 1 3.0E-01
6 : -6.66E+01 3.94E-03 0.000 0.4444 0.9000 0.9000 -0.11 1 1 2.5E-01
7 : -9.14E+01 1.47E-03 0.000 0.3745 0.9000 0.9000 -0.05 1 1 1.6E-01
8 : -1.30E+02 5.89E-04 0.000 0.3998 0.9000 0.9000 -0.15 1 1 1.2E-01
9 : -1.86E+02 2.00E-04 0.000 0.3396 0.9000 0.9000 -0.16 1 1 8.0E-02
10 : -2.62E+02 7.54E-05 0.000 0.3766 0.9000 0.9000 -0.19 1 1 6.0E-02
11 : -3.64E+02 2.75E-05 0.000 0.3651 0.9000 0.9000 -0.13 1 1 4.0E-02
12 : -5.12E+02 1.05E-05 0.000 0.3807 0.9000 0.9000 -0.20 1 1 3.1E-02
13 : -6.97E+02 3.90E-06 0.000 0.3721 0.9000 0.9000 -0.13 1 1 2.0E-02
14 : -9.59E+02 1.53E-06 0.000 0.3937 0.9000 0.9000 -0.18 1 1 1.6E-02
15 : -1.31E+03 5.69E-07 0.000 0.3705 0.9000 0.9000 -0.12 1 3 1.1E-02
16 : -1.31E+03 9.98E-08 0.000 0.1756 0.9000 0.0000 -0.18 1 3 9.3E-03
17 : -1.95E+03 3.16E-08 0.000 0.3170 0.9058 0.9000 -0.55 3 3 5.6E-03
18 : -2.72E+03 1.10E-08 0.000 0.3483 0.9040 0.9000 -0.36 3 3 4.0E-03
19 : -3.85E+03 4.09E-09 0.000 0.3713 0.9000 0.8955 -0.33 3 3 2.9E-03
20 : -5.08E+03 1.63E-09 0.000 0.3989 0.9000 0.8029 -0.20 2 2 2.2E-03
21 : -6.41E+03 6.06E-10 0.000 0.3712 0.9117 0.9000 -0.12 2 2 1.4E-03
22 : -7.83E+03 3.10E-10 0.000 0.5111 0.9000 0.9062 -0.10 2 2 1.1E-03
23 : -9.08E+03 1.95E-10 0.000 0.6287 0.9000 0.5940 -0.12 2 2 9.9E-04
24 : -1.07E+04 8.51E-11 0.000 0.4370 0.9151 0.9000 -0.02 2 2 6.8E-04
25 : -1.28E+04 4.72E-11 0.000 0.5546 0.9000 0.8398 -0.07 2 2 5.5E-04
26 : -1.45E+04 2.92E-11 0.000 0.6183 0.9000 0.9000 0.00 6 6 4.7E-04
27 : -1.67E+04 1.53E-11 0.000 0.5232 0.9026 0.9000 0.07 6 6 3.5E-04
28 : -1.89E+04 9.67E-12 0.000 0.6335 0.9000 0.5832 0.02 6 6 3.0E-04
29 : -2.14E+04 4.86E-12 0.000 0.5025 0.9090 0.9000 0.13 7 6 2.1E-04
30 : -2.43E+04 2.96E-12 0.000 0.6087 0.9000 0.6349 0.08 7 7 1.8E-04
31 : -2.73E+04 1.55E-12 0.000 0.5228 0.9031 0.9000 0.22 7 7 1.3E-04
32 : -3.02E+04 9.69E-13 0.000 0.6265 0.9000 0.5668 0.15 7 7 1.1E-04
33 : -3.34E+04 4.80E-13 0.000 0.4955 0.9087 0.9000 0.29 7 7 7.4E-05
34 : -3.67E+04 2.90E-13 0.000 0.6046 0.9000 0.6430 0.24 7 7 6.0E-05
35 : -3.99E+04 1.48E-13 0.000 0.5103 0.9000 0.9000 0.40 7 7 4.0E-05
36 : -4.22E+04 9.35E-14 0.000 0.6315 0.9000 0.5694 0.36 8 8 3.2E-05
37 : -4.47E+04 4.25E-14 0.000 0.4540 0.9066 0.9000 0.52 9 9 1.8E-05
38 : -4.64E+04 2.48E-14 0.000 0.5848 0.9000 0.6839 0.55 11 10 1.3E-05
39 : -4.77E+04 1.13E-14 0.000 0.4539 0.9000 0.8663 0.70 12 11 6.6E-06
40 : -4.83E+04 5.89E-15 0.000 0.5228 0.9000 0.6903 0.77 13 18 3.8E-06
41 : -4.88E+04 1.86E-15 0.000 0.3149 0.9031 0.9000 0.86 13 13 1.3E-06
42 : -4.89E+04 1.05E-15 0.000 0.5637 0.9000 0.6344 0.83 16 15 8.0E-07
Run into numerical problems.
iter seconds digits c*x b*y
42 0.5 Inf -4.8895099743e+04 -4.8885076907e+04
|Ax-b| = 2.3e-06, [Ay-c]_+ = 4.7E-07, |x|= 1.1e+09, |y|= 2.1e+04
Detailed timing (sec)
Pre IPM Post
4.200E-02 6.450E-01 9.002E-03
Max-norms: ||b||=1, ||c|| = 2,
Cholesky |add|=4, |skip| = 0, ||L.L|| = 1.69885e+06.
------------------------------------------------------------
Status: Inaccurate/Solved
Optimal value (cvx_optval): +48885.1
Calling SeDuMi 1.3.4: 400 variables, 197 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 = 197, order n = 62, dim = 785, blocks = 10
nnz(A) = 1943 + 0, nnz(ADA) = 38809, nnz(L) = 19503
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 4.31E-01 0.000
1 : -4.39E+00 2.22E-01 0.000 0.5162 0.9000 0.9000 3.96 1 1 1.9E+00
2 : -1.60E+01 1.09E-01 0.000 0.4910 0.9000 0.9000 0.70 1 1 1.3E+00
3 : -2.41E+01 4.38E-02 0.000 0.4009 0.9000 0.9000 0.63 1 1 6.6E-01
4 : -3.31E+01 2.18E-02 0.000 0.4991 0.9000 0.9000 0.24 1 1 4.7E-01
5 : -4.60E+01 8.84E-03 0.000 0.4048 0.9000 0.9000 0.15 1 1 3.0E-01
6 : -6.71E+01 3.83E-03 0.000 0.4336 0.9000 0.9000 -0.10 1 1 2.5E-01
7 : -9.05E+01 1.49E-03 0.000 0.3899 0.9000 0.9000 -0.03 1 1 1.6E-01
8 : -1.25E+02 6.40E-04 0.000 0.4279 0.9000 0.9000 -0.14 1 1 1.2E-01
9 : -1.80E+02 2.19E-04 0.000 0.3419 0.9000 0.9000 -0.16 1 1 8.1E-02
10 : -2.55E+02 8.24E-05 0.000 0.3766 0.9000 0.9000 -0.21 1 1 6.2E-02
11 : -3.53E+02 2.98E-05 0.000 0.3619 0.9000 0.9000 -0.14 1 1 4.1E-02
12 : -4.93E+02 1.19E-05 0.000 0.3989 0.9000 0.9000 -0.21 1 1 3.2E-02
13 : -6.83E+02 4.16E-06 0.000 0.3500 0.9000 0.9000 -0.15 1 1 2.1E-02
14 : -9.60E+02 1.53E-06 0.000 0.3679 0.9000 0.9000 -0.19 1 1 1.6E-02
15 : -1.30E+03 5.80E-07 0.000 0.3792 0.9000 0.9000 -0.12 1 1 1.1E-02
16 : -1.72E+03 2.54E-07 0.000 0.4385 0.9000 0.9000 -0.17 1 1 8.5E-03
17 : -2.32E+03 9.24E-08 0.000 0.3632 0.9000 0.9000 -0.14 1 1 5.6E-03
18 : -3.02E+03 4.06E-08 0.000 0.4390 0.9000 0.9000 -0.16 1 1 4.4E-03
19 : -3.96E+03 1.62E-08 0.000 0.3986 0.9000 0.9000 -0.14 2 2 3.1E-03
20 : -3.96E+03 3.14E-09 0.000 0.1939 0.9000 0.0000 -0.14 2 2 2.8E-03
21 : -5.17E+03 1.04E-09 0.000 0.3322 0.9182 0.9000 -0.39 2 2 1.6E-03
22 : -7.48E+03 3.91E-10 0.000 0.3755 0.9000 0.9098 -0.34 2 2 1.2E-03
23 : -9.05E+03 1.97E-10 0.000 0.5038 0.9000 0.6791 -0.15 2 2 9.9E-04
24 : -1.07E+04 5.70E-11 0.000 0.2895 0.9250 0.9000 0.01 2 2 5.1E-04
25 : -1.28E+04 2.69E-11 0.000 0.4708 0.9012 0.9000 -0.03 2 2 3.7E-04
26 : -1.56E+04 1.36E-11 0.000 0.5078 0.9000 0.7180 -0.06 2 2 3.1E-04
27 : -1.79E+04 6.69E-12 0.000 0.4905 0.9014 0.9000 0.16 2 2 2.2E-04
28 : -2.03E+04 3.94E-12 0.000 0.5887 0.9000 0.5848 0.09 2 2 1.9E-04
29 : -2.28E+04 1.87E-12 0.000 0.4759 0.9104 0.9000 0.22 2 2 1.2E-04
30 : -2.57E+04 1.06E-12 0.000 0.5654 0.9000 0.6731 0.16 6 6 1.0E-04
31 : -2.86E+04 5.35E-13 0.000 0.5052 0.9000 0.8965 0.31 7 7 6.9E-05
32 : -3.10E+04 3.26E-13 0.000 0.6095 0.9000 0.9000 0.25 7 7 5.7E-05
33 : -3.36E+04 1.53E-13 0.000 0.4696 0.9083 0.9000 0.40 7 7 3.4E-05
34 : -3.58E+04 8.82E-14 0.000 0.5758 0.9000 0.6848 0.39 16 17 2.6E-05
35 : -3.76E+04 4.37E-14 0.000 0.4955 0.9000 0.8638 0.55 18 15 1.6E-05
36 : -3.76E+04 4.36E-14 0.000 0.9971 0.9000 0.9000 0.60 18 18 1.5E-05
37 : -3.87E+04 2.52E-14 0.000 0.5774 0.9000 0.9000 0.60 14 16 1.1E-05
38 : -3.96E+04 1.07E-14 0.000 0.4273 0.9000 0.9000 0.73 23 17 5.1E-06
Run into numerical problems.
iter seconds digits c*x b*y
38 0.8 Inf -3.9652026337e+04 -3.9613134331e+04
|Ax-b| = 9.0e-06, [Ay-c]_+ = 3.4E-06, |x|= 6.6e+08, |y|= 2.0e+04
Detailed timing (sec)
Pre IPM Post
1.700E-02 4.170E-01 3.993E-03
Max-norms: ||b||=1, ||c|| = 2,
Cholesky |add|=3, |skip| = 0, ||L.L|| = 999678.
------------------------------------------------------------
Status: Inaccurate/Solved
Optimal value (cvx_optval): +39613.1
Calling SeDuMi 1.3.4: 400 variables, 197 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 = 197, order n = 62, dim = 785, blocks = 10
nnz(A) = 1943 + 0, nnz(ADA) = 38809, nnz(L) = 19503
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 4.31E-01 0.000
1 : -4.39E+00 2.22E-01 0.000 0.5162 0.9000 0.9000 3.96 1 1 1.9E+00
2 : -1.60E+01 1.09E-01 0.000 0.4912 0.9000 0.9000 0.70 1 1 1.3E+00
3 : -2.41E+01 4.38E-02 0.000 0.4007 0.9000 0.9000 0.63 1 1 6.6E-01
4 : -3.31E+01 2.18E-02 0.000 0.4990 0.9000 0.9000 0.24 1 1 4.7E-01
5 : -4.59E+01 8.87E-03 0.000 0.4061 0.9000 0.9000 0.15 1 1 3.0E-01
6 : -6.64E+01 3.89E-03 0.000 0.4391 0.9000 0.9000 -0.10 1 1 2.5E-01
7 : -9.05E+01 1.49E-03 0.000 0.3831 0.9000 0.9000 -0.04 1 1 1.6E-01
8 : -1.25E+02 6.33E-04 0.000 0.4239 0.9000 0.9000 -0.14 1 1 1.2E-01
9 : -1.78E+02 2.25E-04 0.000 0.3556 0.9000 0.9000 -0.16 1 1 8.2E-02
10 : -2.44E+02 9.22E-05 0.000 0.4100 0.9000 0.9000 -0.21 1 1 6.3E-02
11 : -3.39E+02 3.40E-05 0.000 0.3690 0.9000 0.9000 -0.17 1 1 4.3E-02
12 : -4.72E+02 1.32E-05 0.000 0.3865 0.9000 0.9000 -0.22 1 1 3.3E-02
13 : -6.50E+02 4.89E-06 0.000 0.3716 0.9000 0.9000 -0.17 1 1 2.2E-02
14 : -8.89E+02 1.91E-06 0.000 0.3908 0.9000 0.9000 -0.19 1 1 1.7E-02
15 : -1.22E+03 7.06E-07 0.000 0.3697 0.9000 0.9000 -0.15 1 1 1.1E-02
16 : -1.68E+03 2.67E-07 0.000 0.3774 0.9000 0.9000 -0.19 1 1 8.5E-03
17 : -2.25E+03 1.02E-07 0.000 0.3827 0.9000 0.9000 -0.12 1 1 5.8E-03
18 : -2.90E+03 4.64E-08 0.000 0.4551 0.9000 0.9000 -0.16 2 1 4.6E-03
19 : -3.78E+03 1.85E-08 0.000 0.3981 0.9000 0.9000 -0.13 2 2 3.2E-03
20 : -3.78E+03 3.57E-09 0.000 0.1930 0.9000 0.0000 -0.15 2 2 2.8E-03
21 : -5.07E+03 1.21E-09 0.000 0.3394 0.9131 0.9000 -0.42 2 2 1.7E-03
22 : -7.06E+03 4.71E-10 0.000 0.3887 0.9000 0.9128 -0.32 2 2 1.3E-03
23 : -8.74E+03 2.30E-10 0.000 0.4889 0.9000 0.7245 -0.20 2 2 1.0E-03
24 : -1.04E+04 7.59E-11 0.000 0.3299 0.9208 0.9000 0.00 2 2 5.8E-04
25 : -1.25E+04 3.64E-11 0.000 0.4803 0.9000 0.9035 -0.04 4 4 4.3E-04
26 : -1.49E+04 2.02E-11 0.000 0.5537 0.9000 0.6630 -0.06 4 5 3.7E-04
27 : -1.71E+04 9.87E-12 0.000 0.4893 0.9061 0.9000 0.13 4 5 2.6E-04
28 : -1.95E+04 5.82E-12 0.000 0.5894 0.9000 0.6433 0.07 5 5 2.2E-04
29 : -2.21E+04 2.95E-12 0.000 0.5067 0.9031 0.9000 0.19 5 5 1.5E-04
30 : -2.48E+04 1.79E-12 0.000 0.6057 0.9000 0.5897 0.12 7 6 1.3E-04
31 : -2.76E+04 8.75E-13 0.000 0.4897 0.9076 0.9000 0.26 6 6 8.8E-05
32 : -3.06E+04 5.15E-13 0.000 0.5887 0.9000 0.6416 0.20 6 7 7.2E-05
33 : -3.35E+04 2.56E-13 0.000 0.4981 0.9015 0.9000 0.35 7 6 4.7E-05
34 : -3.59E+04 1.57E-13 0.000 0.6123 0.9000 0.5896 0.32 6 6 3.8E-05
35 : -3.82E+04 7.28E-14 0.000 0.4638 0.9056 0.9000 0.47 7 7 2.2E-05
36 : -3.99E+04 4.28E-14 0.000 0.5875 0.9000 0.6671 0.49 18 17 1.6E-05
37 : -4.13E+04 1.97E-14 0.000 0.4607 0.9000 0.9000 0.65 16 17 8.7E-06
38 : -4.20E+04 1.11E-14 0.000 0.5650 0.9000 0.9000 0.71 26 25 5.6E-06
Run into numerical problems.
iter seconds digits c*x b*y
38 0.6 Inf -4.1998215677e+04 -4.1953394582e+04
|Ax-b| = 1.2e-05, [Ay-c]_+ = 3.4E-06, |x|= 7.6e+08, |y|= 2.0e+04
Detailed timing (sec)
Pre IPM Post
1.500E-02 3.790E-01 4.999E-03
Max-norms: ||b||=1, ||c|| = 2,
Cholesky |add|=3, |skip| = 0, ||L.L|| = 1.10863e+06.
------------------------------------------------------------
Status: Inaccurate/Solved
Optimal value (cvx_optval): +41953.4
Calling SeDuMi 1.3.4: 400 variables, 197 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 = 197, order n = 62, dim = 785, blocks = 10
nnz(A) = 1943 + 0, nnz(ADA) = 38809, nnz(L) = 19503
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 4.31E-01 0.000
1 : -4.39E+00 2.22E-01 0.000 0.5162 0.9000 0.9000 3.96 1 1 1.9E+00
2 : -1.60E+01 1.09E-01 0.000 0.4910 0.9000 0.9000 0.70 1 1 1.3E+00
3 : -2.40E+01 4.38E-02 0.000 0.4009 0.9000 0.9000 0.63 1 1 6.6E-01
4 : -3.31E+01 2.18E-02 0.000 0.4991 0.9000 0.9000 0.24 1 1 4.7E-01
5 : -4.59E+01 8.84E-03 0.000 0.4049 0.9000 0.9000 0.15 1 1 3.0E-01
6 : -6.69E+01 3.83E-03 0.000 0.4335 0.9000 0.9000 -0.10 1 1 2.5E-01
7 : -9.03E+01 1.50E-03 0.000 0.3901 0.9000 0.9000 -0.03 1 1 1.6E-01
8 : -1.24E+02 6.44E-04 0.000 0.4308 0.9000 0.9000 -0.13 1 1 1.2E-01
9 : -1.77E+02 2.23E-04 0.000 0.3458 0.9000 0.9000 -0.15 1 1 8.1E-02
10 : -2.49E+02 8.66E-05 0.000 0.3886 0.9000 0.9000 -0.21 1 1 6.2E-02
11 : -3.47E+02 3.13E-05 0.000 0.3613 0.9000 0.9000 -0.15 1 1 4.1E-02
12 : -4.92E+02 1.18E-05 0.000 0.3788 0.9000 0.9000 -0.22 1 1 3.2E-02
13 : -6.72E+02 4.39E-06 0.000 0.3708 0.9000 0.9000 -0.14 1 1 2.1E-02
14 : -9.18E+02 1.75E-06 0.000 0.3995 0.9000 0.9000 -0.19 1 1 1.6E-02
15 : -1.26E+03 6.38E-07 0.000 0.3638 0.9000 0.9000 -0.14 1 3 1.1E-02
16 : -1.26E+03 1.08E-07 0.000 0.1692 0.9000 0.0000 -0.19 1 3 9.6E-03
17 : -1.89E+03 3.44E-08 0.000 0.3180 0.9056 0.9000 -0.55 3 3 5.7E-03
18 : -2.68E+03 1.11E-08 0.000 0.3234 0.9049 0.9000 -0.37 3 3 4.0E-03
19 : -3.79E+03 4.06E-09 0.000 0.3653 0.9000 0.9094 -0.32 3 3 2.9E-03
20 : -4.97E+03 1.70E-09 0.000 0.4193 0.9000 0.7656 -0.21 4 4 2.2E-03
21 : -6.22E+03 6.00E-10 0.000 0.3526 0.9148 0.9000 -0.10 4 4 1.4E-03
22 : -7.45E+03 3.12E-10 0.000 0.5194 0.9000 0.9009 -0.07 4 4 1.1E-03
23 : -8.79E+03 1.87E-10 0.000 0.6009 0.9000 0.6714 -0.10 4 4 9.2E-04
24 : -1.03E+04 9.39E-11 0.000 0.5014 0.9033 0.9000 0.02 4 4 6.7E-04
25 : -1.17E+04 5.87E-11 0.000 0.6256 0.9000 0.6499 -0.02 4 4 5.8E-04
26 : -1.35E+04 3.08E-11 0.000 0.5238 0.9030 0.9000 0.06 5 5 4.3E-04
27 : -1.52E+04 1.98E-11 0.000 0.6422 0.9000 0.6078 0.02 5 5 3.7E-04
28 : -1.72E+04 1.04E-11 0.000 0.5287 0.9056 0.9000 0.12 5 6 2.7E-04
29 : -1.93E+04 6.64E-12 0.000 0.6360 0.9000 0.6063 0.07 9 9 2.4E-04
30 : -2.17E+04 3.53E-12 0.000 0.5308 0.9048 0.9000 0.19 11 12 1.7E-04
31 : -2.41E+04 2.23E-12 0.000 0.6326 0.9000 0.5864 0.12 12 12 1.5E-04
32 : -2.68E+04 1.15E-12 0.000 0.5161 0.9060 0.9000 0.26 11 10 1.0E-04
33 : -2.95E+04 7.12E-13 0.000 0.6187 0.9000 0.6062 0.19 12 12 8.5E-05
34 : -3.24E+04 3.62E-13 0.000 0.5076 0.9037 0.9000 0.34 6 7 5.7E-05
35 : -3.48E+04 2.24E-13 0.000 0.6195 0.9000 0.6009 0.29 15 15 4.6E-05
36 : -3.73E+04 1.09E-13 0.000 0.4862 0.9037 0.9000 0.45 15 14 2.8E-05
37 : -3.91E+04 6.66E-14 0.000 0.6115 0.9000 0.6267 0.44 13 16 2.2E-05
38 : -4.07E+04 3.07E-14 0.000 0.4607 0.9013 0.9000 0.60 14 16 1.2E-05
39 : -4.16E+04 1.83E-14 0.000 0.5978 0.9000 0.6173 0.64 18 16 8.3E-06
40 : -4.23E+04 6.77E-15 0.000 0.3690 0.9051 0.9000 0.78 17 26 3.4E-06
Run into numerical problems.
iter seconds digits c*x b*y
40 0.5 Inf -4.2354411625e+04 -4.2281456178e+04
|Ax-b| = 7.1e-06, [Ay-c]_+ = 2.1E-06, |x|= 7.8e+08, |y|= 1.8e+04
Detailed timing (sec)
Pre IPM Post
1.200E-02 4.140E-01 3.007E-03
Max-norms: ||b||=1, ||c|| = 2,
Cholesky |add|=3, |skip| = 0, ||L.L|| = 1.23792e+06.
------------------------------------------------------------
Status: Inaccurate/Solved
Optimal value (cvx_optval): +42281.5
Calling SeDuMi 1.3.4: 400 variables, 197 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 = 197, order n = 62, dim = 785, blocks = 10
nnz(A) = 1943 + 0, nnz(ADA) = 38809, nnz(L) = 19503
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 4.31E-01 0.000
1 : -4.39E+00 2.22E-01 0.000 0.5162 0.9000 0.9000 3.96 1 1 1.9E+00
2 : -1.60E+01 1.09E-01 0.000 0.4909 0.9000 0.9000 0.70 1 1 1.3E+00
3 : -2.40E+01 4.38E-02 0.000 0.4009 0.9000 0.9000 0.63 1 1 6.6E-01
4 : -3.31E+01 2.19E-02 0.000 0.4993 0.9000 0.9000 0.24 1 1 4.7E-01
5 : -4.59E+01 8.84E-03 0.000 0.4045 0.9000 0.9000 0.15 1 1 3.0E-01
6 : -6.70E+01 3.82E-03 0.000 0.4317 0.9000 0.9000 -0.10 1 1 2.4E-01
7 : -9.02E+01 1.50E-03 0.000 0.3928 0.9000 0.9000 -0.02 1 1 1.5E-01
8 : -1.23E+02 6.53E-04 0.000 0.4360 0.9000 0.9000 -0.13 1 1 1.2E-01
9 : -1.76E+02 2.24E-04 0.000 0.3421 0.9000 0.9000 -0.15 1 1 8.0E-02
10 : -2.50E+02 8.47E-05 0.000 0.3787 0.9000 0.9000 -0.21 1 1 6.0E-02
11 : -3.45E+02 3.10E-05 0.000 0.3658 0.9000 0.9000 -0.14 1 1 4.0E-02
12 : -4.80E+02 1.25E-05 0.000 0.4045 0.9000 0.9000 -0.21 1 1 3.2E-02
13 : -6.61E+02 4.52E-06 0.000 0.3611 0.9000 0.9000 -0.16 1 1 2.1E-02
14 : -9.11E+02 1.77E-06 0.000 0.3907 0.9000 0.9000 -0.20 1 1 1.6E-02
15 : -1.26E+03 6.40E-07 0.000 0.3621 0.9000 0.9000 -0.14 1 1 1.1E-02
16 : -1.71E+03 2.59E-07 0.000 0.4045 0.9000 0.9000 -0.19 1 1 8.6E-03
17 : -2.29E+03 9.52E-08 0.000 0.3677 0.9000 0.9000 -0.12 1 1 5.6E-03
18 : -3.02E+03 4.08E-08 0.000 0.4284 0.9000 0.9000 -0.16 3 3 4.4E-03
19 : -3.95E+03 4.42E-09 0.000 0.1084 0.8455 0.9000 -0.13 3 3 3.0E-03
20 : -4.89E+03 2.22E-09 0.000 0.5028 0.9000 0.7270 -0.14 2 2 2.4E-03
21 : -6.14E+03 8.89E-10 0.000 0.3996 0.9070 0.9000 -0.10 2 2 1.7E-03
22 : -7.43E+03 4.69E-10 0.000 0.5279 0.9000 0.8427 -0.09 2 2 1.3E-03
23 : -8.59E+03 2.77E-10 0.000 0.5896 0.9000 0.9000 -0.05 2 2 1.1E-03
24 : -1.01E+04 1.40E-10 0.000 0.5069 0.9033 0.9000 0.01 2 2 8.1E-04
25 : -1.14E+04 8.92E-11 0.000 0.6362 0.9000 0.6446 -0.02 2 2 7.0E-04
26 : -1.31E+04 4.78E-11 0.000 0.5357 0.9016 0.9000 0.07 2 2 5.3E-04
27 : -1.47E+04 3.13E-11 0.000 0.6558 0.9000 0.5842 0.03 2 2 4.6E-04
28 : -1.66E+04 1.64E-11 0.000 0.5228 0.9079 0.9000 0.13 2 2 3.3E-04
29 : -1.87E+04 1.04E-11 0.000 0.6338 0.9000 0.6241 0.07 2 2 2.9E-04
30 : -2.10E+04 5.58E-12 0.000 0.5377 0.9021 0.9000 0.21 2 2 2.1E-04
31 : -2.33E+04 3.58E-12 0.000 0.6415 0.9000 0.5574 0.13 2 2 1.8E-04
32 : -2.59E+04 1.78E-12 0.000 0.4979 0.9085 0.9000 0.26 2 2 1.2E-04
33 : -2.86E+04 1.09E-12 0.000 0.6093 0.9000 0.6348 0.20 2 2 1.0E-04
34 : -3.13E+04 5.56E-13 0.000 0.5117 0.9011 0.9000 0.35 2 2 6.9E-05
35 : -3.35E+04 3.49E-13 0.000 0.6272 0.9000 0.5745 0.30 3 3 5.6E-05
36 : -3.59E+04 1.63E-13 0.000 0.4662 0.9062 0.9000 0.46 4 4 3.3E-05
37 : -3.76E+04 9.75E-14 0.000 0.6002 0.9000 0.6634 0.46 5 6 2.5E-05
38 : -3.90E+04 4.63E-14 0.000 0.4749 0.9000 0.8797 0.62 5 6 1.4E-05
39 : -3.98E+04 2.69E-14 0.000 0.5802 0.9000 0.6478 0.67 7 8 9.3E-06
40 : -4.04E+04 1.01E-14 0.000 0.3748 0.9030 0.9000 0.80 8 8 3.9E-06
41 : -4.07E+04 4.91E-15 0.000 0.4877 0.9000 0.6781 0.85 17 25 2.0E-06
42 : -4.08E+04 1.19E-15 0.000 0.2423 0.9252 0.9000 0.90 22 26 6.5E-07
Run into numerical problems.
iter seconds digits c*x b*y
42 0.8 Inf -4.0825750205e+04 -4.0776373349e+04
|Ax-b| = 1.1e-06, [Ay-c]_+ = 4.3E-07, |x|= 8.1e+08, |y|= 1.6e+04
Detailed timing (sec)
Pre IPM Post
5.301E-02 4.280E-01 7.001E-03
Max-norms: ||b||=1, ||c|| = 2,
Cholesky |add|=3, |skip| = 0, ||L.L|| = 1.57156e+06.
------------------------------------------------------------
Status: Inaccurate/Solved
Optimal value (cvx_optval): +40776.4
Calling SeDuMi 1.3.4: 400 variables, 197 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 = 197, order n = 62, dim = 785, blocks = 10
nnz(A) = 1943 + 0, nnz(ADA) = 38809, nnz(L) = 19503
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 4.31E-01 0.000
1 : -4.39E+00 2.22E-01 0.000 0.5162 0.9000 0.9000 3.96 1 1 1.9E+00
2 : -1.60E+01 1.09E-01 0.000 0.4909 0.9000 0.9000 0.70 1 1 1.3E+00
3 : -2.40E+01 4.38E-02 0.000 0.4009 0.9000 0.9000 0.63 1 1 6.6E-01
4 : -3.31E+01 2.19E-02 0.000 0.4993 0.9000 0.9000 0.24 1 1 4.7E-01
5 : -4.59E+01 8.84E-03 0.000 0.4045 0.9000 0.9000 0.15 1 1 3.0E-01
6 : -6.70E+01 3.82E-03 0.000 0.4318 0.9000 0.9000 -0.10 1 1 2.4E-01
7 : -9.02E+01 1.50E-03 0.000 0.3926 0.9000 0.9000 -0.02 1 1 1.5E-01
8 : -1.24E+02 6.52E-04 0.000 0.4353 0.9000 0.9000 -0.13 1 1 1.2E-01
9 : -1.76E+02 2.23E-04 0.000 0.3424 0.9000 0.9000 -0.15 1 1 8.0E-02
10 : -2.50E+02 8.47E-05 0.000 0.3794 0.9000 0.9000 -0.21 1 1 6.1E-02
11 : -3.46E+02 3.09E-05 0.000 0.3647 0.9000 0.9000 -0.14 1 1 4.0E-02
12 : -4.82E+02 1.24E-05 0.000 0.4020 0.9000 0.9000 -0.21 1 1 3.2E-02
13 : -6.66E+02 4.45E-06 0.000 0.3581 0.9000 0.9000 -0.16 1 1 2.1E-02
14 : -9.24E+02 1.70E-06 0.000 0.3828 0.9000 0.9000 -0.19 1 1 1.6E-02
15 : -1.27E+03 6.21E-07 0.000 0.3650 0.9000 0.9000 -0.13 1 1 1.1E-02
16 : -1.71E+03 2.59E-07 0.000 0.4174 0.9000 0.9000 -0.19 1 1 8.6E-03
17 : -2.30E+03 9.46E-08 0.000 0.3649 0.9000 0.9000 -0.13 1 1 5.6E-03
18 : -3.02E+03 4.05E-08 0.000 0.4283 0.9000 0.9000 -0.16 1 1 4.4E-03
19 : -3.97E+03 1.60E-08 0.000 0.3936 0.9000 0.9000 -0.14 1 2 3.0E-03
20 : -4.88E+03 8.14E-09 0.000 0.5104 0.9000 0.9000 -0.14 2 2 2.5E-03
21 : -6.10E+03 9.84E-10 0.000 0.1208 0.8391 0.9000 -0.10 4 4 1.8E-03
22 : -7.24E+03 5.52E-10 0.000 0.5615 0.9000 0.6689 -0.12 4 4 1.5E-03
23 : -8.73E+03 2.33E-10 0.000 0.4220 0.9111 0.9000 -0.05 4 4 9.9E-04
24 : -1.04E+04 1.29E-10 0.000 0.5548 0.9000 0.8467 -0.05 4 4 8.0E-04
25 : -1.18E+04 8.08E-11 0.000 0.6246 0.9000 0.6612 0.01 4 4 6.8E-04
26 : -1.35E+04 4.26E-11 0.000 0.5268 0.9038 0.9000 0.09 5 5 5.0E-04
27 : -1.52E+04 2.73E-11 0.000 0.6421 0.9000 0.6056 0.04 5 5 4.4E-04
28 : -1.72E+04 1.44E-11 0.000 0.5265 0.9045 0.9000 0.14 5 6 3.2E-04
29 : -1.93E+04 9.13E-12 0.000 0.6346 0.9000 0.5877 0.08 6 6 2.8E-04
30 : -2.17E+04 4.67E-12 0.000 0.5113 0.9068 0.9000 0.21 6 6 1.9E-04
31 : -2.42E+04 2.88E-12 0.000 0.6179 0.9000 0.6054 0.14 6 6 1.7E-04
32 : -2.69E+04 1.47E-12 0.000 0.5084 0.9046 0.9000 0.28 6 6 1.1E-04
33 : -2.95E+04 9.05E-13 0.000 0.6172 0.9000 0.5929 0.21 6 6 9.5E-05
34 : -3.22E+04 4.43E-13 0.000 0.4898 0.9052 0.9000 0.36 6 6 6.1E-05
35 : -3.45E+04 2.70E-13 0.000 0.6101 0.9000 0.6236 0.33 6 7 4.9E-05
36 : -3.67E+04 1.31E-13 0.000 0.4832 0.9017 0.9000 0.49 7 7 2.9E-05
37 : -3.82E+04 8.05E-14 0.000 0.6159 0.9000 0.6071 0.49 7 7 2.2E-05
38 : -3.95E+04 3.46E-14 0.000 0.4301 0.9038 0.9000 0.65 7 7 1.1E-05
39 : -4.02E+04 1.98E-14 0.000 0.5709 0.9000 0.6629 0.70 7 7 7.3E-06
40 : -4.07E+04 7.05E-15 0.000 0.3567 0.9020 0.9000 0.83 12 11 2.9E-06
Run into numerical problems.
iter seconds digits c*x b*y
40 0.5 Inf -4.0714337278e+04 -4.0684345949e+04
|Ax-b| = 7.3e-06, [Ay-c]_+ = 1.4E-06, |x|= 7.6e+08, |y|= 1.6e+04
Detailed timing (sec)
Pre IPM Post
1.200E-02 3.860E-01 3.007E-03
Max-norms: ||b||=1, ||c|| = 2,
Cholesky |add|=3, |skip| = 0, ||L.L|| = 1.03461e+06.
------------------------------------------------------------
Status: Inaccurate/Solved
Optimal value (cvx_optval): +40684.3
The problem solved isļ¼
After searching the relevant posts in the forum, I believe that the Inaccurate/Solved problem is caused by the large difference in the magnitude of some parameters, which causes cvx to be troubled in terms of accuracy. But how do I troubleshoot these problems?I would appreciate your any suggestion. Thank you!