Status : Inaccurate/Solved

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 τ
    values.taoCOMUL=10^(10/10);   % Upstream user SNR limit τ
    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 is:


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!

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 the solver fails, or makes erroneous determination of infeasibility or unboundedness.

https://twitter.com/themarklstone/status/1586795881168265216

Don’t apply crude, unsafeguarded (no Trust Region or Line Search) Successive Convex Approximation (SCA) to a new problem … unless your name happens to be Stephen Boyd.

There’s a reason high quality non-convex nonlinear optimization solvers are more than 10 lines long.

Bad initial scaling might be making things worse. .Try to change the units to keep all input data within a small number of orders of magnitude of one. But even if the input data for the first iteration of SCA is well-scaled, the input data on later iterations might become badly scaled because SCA might produce wilder and wilder solutions, which become input data for the next iteration.

Mosek might do better than SDPT3 at handling numerically difficult CVX optimization problems… But even Mosek can’t make SCA always work well, because the SCA algorithm itself is unreliable, no matter what solver is used.

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Thank you so much Mark! The sudumi showd ‘Status : Inaccurate/Solved’ ,and I replaced the mosek solver, it showed an error

Calling Mosek 9.1.9: 409 variables, 200 equality constraints
   For improved efficiency, Mosek is solving the dual problem.
------------------------------------------------------------

MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86

MOSEK warning 710: #3 (nearly) zero elements are specified in sparse col '' (2) of matrix 'A'.
MOSEK warning 710: #4 (nearly) zero elements are specified in sparse col '' (3) of matrix 'A'.
Problem
  Name                   :                 
  Objective sense        : min             
  Type                   : CONIC (conic optimization problem)
  Constraints            : 200             
  Cones                  : 6               
  Scalar variables       : 25              
  Matrix variables       : 6               
  Integer variables      : 0               

Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries                  : 1                 time                   : 0.00            
Lin. dep.  - tries                  : 1                 time                   : 0.00            
Lin. dep.  - number                 : 0               
Presolve terminated. Time: 0.00    
Problem
  Name                   :                 
  Objective sense        : min             
  Type                   : CONIC (conic optimization problem)
  Constraints            : 200             
  Cones                  : 6               
  Scalar variables       : 25              
  Matrix variables       : 6               
  Integer variables      : 0               

Optimizer  - threads                : 14              
Optimizer  - solved problem         : the primal      
Optimizer  - Constraints            : 194
Optimizer  - Cones                  : 6
Optimizer  - Scalar variables       : 22                conic                  : 18              
Optimizer  - Semi-definite variables: 6                 scalarized             : 816             
Factor     - setup time             : 0.00              dense det. time        : 0.00            
Factor     - ML order time          : 0.00              GP order time          : 0.00            
Factor     - nonzeros before factor : 1.13e+04          after factor           : 1.13e+04        
Factor     - dense dim.             : 11                flops                  : 1.14e+06        
ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME  
0   3.5e+00  8.6e+02  1.0e+00  0.00e+00   9.963109181e-04   0.000000000e+00   1.0e+00  0.00  
1   1.0e+00  2.5e+02  5.5e-01  -1.02e+00  -6.072104850e+01  -5.818830976e+01  2.9e-01  0.00  
2   5.0e-02  1.2e+01  1.7e-01  -1.05e+00  -3.419547914e+03  -3.273045169e+03  1.4e-02  0.00  
3   1.1e-02  2.7e+00  2.3e-01  -2.07e+00  -7.135674717e+04  -6.580541431e+04  3.1e-03  0.00  
4   3.9e-03  9.5e-01  7.6e-02  -1.83e+00  -6.827734041e+04  -6.361277118e+04  1.1e-03  0.00  
5   2.4e-03  5.9e-01  7.6e-03  1.80e+00   -3.219644101e+04  -3.207341674e+04  6.8e-04  0.00  
6   8.7e-04  2.1e-01  2.3e-03  2.26e+00   -1.575441996e+04  -1.567058299e+04  2.5e-04  0.00  
7   3.5e-04  8.5e-02  8.4e-04  9.00e-01   -1.570419922e+04  -1.563166839e+04  9.9e-05  0.00  
8   1.1e-04  2.6e-02  1.5e-04  1.01e+00   -1.386835997e+04  -1.384596315e+04  3.1e-05  0.00  
9   3.7e-05  9.1e-03  3.9e-05  6.21e-01   -1.377865126e+04  -1.376520738e+04  1.1e-05  0.00  
10  1.1e-05  2.6e-03  1.0e-05  4.19e-01   -1.407717787e+04  -1.406580173e+04  3.0e-06  0.00  
11  4.9e-06  1.2e-03  4.1e-06  3.75e-01   -1.420756249e+04  -1.419901460e+04  1.4e-06  0.00  
12  1.5e-06  3.6e-04  1.4e-06  6.74e-02   -1.477147439e+04  -1.476029497e+04  4.2e-07  0.02  
13  8.4e-07  2.1e-04  8.6e-07  -3.49e-02  -1.513037785e+04  -1.511757290e+04  2.4e-07  0.02  
14  4.0e-07  9.8e-05  4.2e-07  -9.80e-02  -1.561346370e+04  -1.559988936e+04  1.1e-07  0.02  
15  2.7e-07  6.7e-05  3.2e-07  -1.80e-01  -1.598652953e+04  -1.596990333e+04  7.8e-08  0.02  
16  1.0e-07  2.4e-05  1.2e-07  -1.85e-01  -1.693540305e+04  -1.691682966e+04  2.8e-08  0.02  
17  4.7e-08  1.2e-05  6.9e-08  -1.83e-01  -1.803745097e+04  -1.801145727e+04  1.3e-08  0.02  
18  1.6e-08  3.9e-06  2.3e-08  -8.16e-02  -1.941767876e+04  -1.939251097e+04  4.5e-09  0.02  
19  6.4e-09  1.6e-06  1.1e-08  -1.02e-01  -2.130494728e+04  -2.126893858e+04  1.8e-09  0.02  
20  2.3e-09  5.7e-07  3.8e-09  2.30e-02   -2.303158158e+04  -2.299901917e+04  6.6e-10  0.02  
21  1.0e-09  2.5e-07  2.2e-09  -1.45e-01  -2.598164179e+04  -2.592604880e+04  2.9e-10  0.02  
22  3.5e-10  8.5e-08  7.0e-10  -9.21e-03  -2.895661890e+04  -2.890611429e+04  9.9e-11  0.02  
23  1.2e-10  4.3e-08  3.4e-10  -1.80e-01  -3.514607382e+04  -3.505036542e+04  3.5e-11  0.02  
24  4.2e-11  2.1e-08  9.8e-11  1.50e-01   -3.923325901e+04  -3.916692646e+04  1.2e-11  0.02  
25  3.9e-11  2.0e-08  9.2e-11  -4.28e-03  -3.970346073e+04  -3.963480484e+04  1.1e-11  0.02  
26  3.8e-11  1.9e-08  9.1e-11  -3.57e-02  -3.976196817e+04  -3.969309903e+04  1.1e-11  0.03  
27  3.5e-11  1.8e-08  8.5e-11  -3.85e-02  -4.025854753e+04  -4.018792100e+04  1.0e-11  0.03  
28  3.5e-11  1.7e-08  8.3e-11  -4.92e-02  -4.038077549e+04  -4.030981026e+04  9.9e-12  0.03  
29  3.3e-11  1.7e-08  8.0e-11  -5.07e-02  -4.063057603e+04  -4.055895669e+04  9.5e-12  0.03  
30  3.3e-11  1.7e-08  7.9e-11  -5.16e-02  -4.069235425e+04  -4.062059122e+04  9.4e-12  0.03  
31  3.1e-11  1.6e-08  7.6e-11  -5.16e-02  -4.094578822e+04  -4.087345302e+04  9.0e-12  0.03  
32  1.8e-11  1.1e-08  2.6e-11  -5.03e-02  -4.841928998e+04  -4.833211186e+04  2.8e-12  0.05  
33  9.5e-12  1.1e-08  2.5e-11  4.69e-01   -4.858679247e+04  -4.850180044e+04  2.7e-12  0.05  
34  9.5e-12  1.1e-08  2.5e-11  4.70e-01   -4.858679247e+04  -4.850180044e+04  2.7e-12  0.05  
35  9.5e-12  1.1e-08  2.5e-11  4.70e-01   -4.858679247e+04  -4.850180044e+04  2.7e-12  0.05  
Optimizer terminated. Time: 0.05    


Interior-point solution summary
  Problem status  : UNKNOWN
  Solution status : UNKNOWN
  Primal.  obj: -4.8586792466e+04   nrm: 3e+10    Viol.  con: 6e-05    var: 0e+00    barvar: 0e+00    cones: 1e-12  
  Dual.    obj: -4.8501800443e+04   nrm: 5e+06    Viol.  con: 0e+00    var: 4e+06    barvar: 2e-05    cones: 0e+00  
Optimizer summary
  Optimizer                 -                        time: 0.05    
    Interior-point          - iterations : 36        time: 0.05    
      Basis identification  -                        time: 0.00    
        Primal              - iterations : 0         time: 0.00    
        Dual                - iterations : 0         time: 0.00    
        Clean primal        - iterations : 0         time: 0.00    
        Clean dual          - iterations : 0         time: 0.00    
    Simplex                 -                        time: 0.00    
      Primal simplex        - iterations : 0         time: 0.00    
      Dual simplex          - iterations : 0         time: 0.00    
    Mixed integer           - relaxations: 0         time: 0.00    

------------------------------------------------------------
Status: Inaccurate/Infeasible
Optimal value (cvx_optval): +Inf
 
Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN. 
> In test>SCA_step (line 103)
In test>SCA_algorithm_1 (line 57)
In test (line 22)
 
Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN. 
> In test>SCA_step (line 106)
In test>SCA_algorithm_1 (line 57)
In test (line 22)
 
Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN. 
> In test>SCA_step (line 109)
In test>SCA_algorithm_1 (line 57)
In test (line 22)
 

aa =

      NaN +    NaNi

Error using  + 
Disciplined convex programming error:
   Illegal operation: {mixed real affine/complex affine} - {invalid}

Error in  -  (line 21)
z = plus( x, y, true, cheat );

Error in test>SCA_step (line 115)
        bb=ar'*F_pre_inv*(F-F_pre)*F_pre_inv*ar

Error in test>SCA_algorithm_1 (line 57)
    [Pmin, V0, V1, V2, pk1, pk2, cvx_status] = SCA_step(para,g1,g2,h1,h2,ar,A0,A1,A2,V0,V1,V2,pk1,pk2);

Error in test (line 22)
[Pmin,V0,V1,V2,pk1,pk2] = SCA_algorithm_1(para,g1,g2,h1,h2,ar,A0,A1,A2);
 

I am in the repetition of a paper simulation, which the authors have done before.The optimization problem is supposed to be solvable, but maybe there are some problems with how I describe it in MATLAB, and maybe in MATLAB the constrains in SCA make the minimize problem unsolvable.

As you can see from the Mosek solution summary the “solution” Mosek produced is actually very bad with large violations (status is in fact unknown), so it is very likely that it is useless for the remainder of your algorithm, and that’s what crashes your further steps. Not to mention that in this case CVX returns no solution, so you are trying to use data which was populated with NaNs. I can only speculate that you are trying to solve a problem which in reality is ill-posed and the numerics are poor, which can be the source of all kinds of issues.

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