mohammad hassan
Mar 7, 2019, 10:57:49 AM3/7/19
to YALMIP
Dear Yohan Löfberg
I'm new in using Yalmip solver.
I have problem 'Numerical problems (SeDuMi-1.3)' in solve linear matrix inequality.
I run the following code
I also send the code file in the attachment.
---------------------------------------------------------------------------
clc
clear all
% Define parameters
A1 = 1e+04 * [-0.0000 0.0000 0.0000 0.0000 0.0000
0 -0.0002 4.4982 0 0
0 0.0000 -0.0003 0.0000 0.0000
0 0.0002 0 -0.0000 0.0001
0 0 0.0002 0 -0.0002];
A2 = 1e+04 * [-0.0000 0.0000 0.0000 0.0000 0.0000
0 -0.0002 4.4982 0 0
0 0.0000 -0.0003 0.0000 0.0000
0 0.0002 0 -4.4976 0.0001
0 0 0.0002 0 -0.0002];
A3 = [-0.0030 0.4640 0.4640 0.4640 0.4640
0 -2.4600 0.0042 0 0
0 0.1000 -2.7510 0.0003 0.2978
0 1.9000 0 -0.4631 1.0622
0 0 2.2910 0 -1.8200];
A4 = 1e+04 * [-0.0000 0.0000 0.0000 0.0000 0.0000
0 -0.0002 0.0000 0 0
0 0.0000 -0.0003 0.0000 0.0000
0 0.0002 0 -4.4976 0.0001
0 0 0.0002 0 -0.0002];
A5 = 1e+05 * [-1.1244 0.0000 0.0000 0.0000 0.0000
0 -0.0000 0.4498 0 0
0 0.0000 -0.0000 0.0000 0.0000
0 0.0000 0 -0.0000 0.0000
0 0 0.0000 0 -0.0000];
A6 = 1e+05 * [-1.1244 0.0000 0.0000 0.0000 0.0000
0 -0.0000 0.4498 0 0
0 0.0000 -0.0000 0.0000 0.0000
0 0.0000 0 -0.4498 0.0000
0 0 0.0000 0 -0.0000];
A7 = 1e+05 * [-1.1244 0.0000 0.0000 0.0000 0.0000
0 -0.0000 0.0000 0 0
0 0.0000 -0.0000 0.0000 0.0000
0 0.0000 0 -0.0000 0.0000
0 0 0.0000 0 -0.0000];
A8 = 1e+05 * [-1.1244 0.0000 0.0000 0.0000 0.0000
0 -0.0000 0.0000 0 0
0 0.0000 -0.0000 0.0000 0.0000
0 0.0000 0 -0.4498 0.0000
0 0 0.0000 0 -0.0000];
B1 = [0 0
0 0
-0.75 0
0 -0.6
0.75 0.6];
B2 = B1;
B3 = B1;
B4 = B1;
B5 = B1;
B6 = B1;
B7 = B1;
B8 = B1;
Pb = sdpvar(5,5);
Kb = sdpvar(2,5);
M1 = A1*Pb+B1*Kb+transpose(A1*Pb+B1*Kb);
M2 = A2*Pb+B2*Kb+transpose(A2*Pb+B2*Kb);
M3 = A3*Pb+B3*Kb+transpose(A3*Pb+B3*Kb);
M4 = A4*Pb+B4*Kb+transpose(A4*Pb+B4*Kb);
M5 = A5*Pb+B5*Kb+transpose(A5*Pb+B5*Kb);
M6 = A6*Pb+B6*Kb+transpose(A6*Pb+B6*Kb);
M7 = A7*Pb+B7*Kb+transpose(A7*Pb+B7*Kb);
M8 = A8*Pb+B8*Kb+transpose(A8*Pb+B8*Kb);
Constraints = [Pb >= 0, M1 <= 0, M2 <= 0, M3 <= 0, M4 <= 0, M5 <= 0, M6 <= 0, M7 <= 0, M8 <= 0];
options = sdpsettings('verbose',1,'solver','sedumi','quadprog.maxiter',100);
sol = optimize(Constraints,[],options);
if sol.problem == 0
% Extract and display value
disp('Pb =')
disp(value(Pb))
disp('Kb =')
disp(value(Kb))
else
disp('Hmm, something went wrong!');
yalmiperror(sol.problem)
end
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In above code 'Pb' must be positive definite matrix.
And I encounter the following error.
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The coefficient matrix is not full row rank, numerical problems may occur.
SeDuMi 1.3 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, theta = 0.250, beta = 0.500
eqs m = 25, order n = 46, dim = 226, blocks = 10
nnz(A) = 378 + 0, nnz(ADA) = 625, nnz(L) = 325
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 7.04E+10 0.000
1 : 0.00E+00 1.46E+10 0.000 0.2074 0.9000 0.9000 1.00 1 0 3.7E+05
2 : 0.00E+00 3.11E+09 0.000 0.2129 0.9000 0.9000 1.00 1 1 7.9E+04
3 : 0.00E+00 5.82E+08 0.000 0.1873 0.9000 0.9000 1.00 1 1 1.5E+04
4 : 0.00E+00 1.42E+07 0.000 0.0243 0.9900 0.9900 1.00 1 1 3.6E+02
5 : 0.00E+00 9.40E+05 0.000 0.0663 0.9900 0.9900 1.00 1 1 2.4E+01
6 : 0.00E+00 3.73E+05 0.000 0.3967 0.9000 0.9000 1.00 1 1 9.5E+00
7 : 0.00E+00 1.06E+05 0.000 0.2835 0.9000 0.9000 1.00 1 1 2.7E+00
8 : 0.00E+00 4.11E+04 0.000 0.3892 0.9000 0.9000 1.00 1 1 1.1E+00
9 : 0.00E+00 1.32E+04 0.000 0.3210 0.9000 0.9000 1.00 1 1 3.4E-01
10 : 0.00E+00 3.46E+03 0.000 0.2623 0.9000 0.9000 1.00 1 1 8.9E-02
11 : 0.00E+00 8.07E+02 0.000 0.2331 0.9000 0.9000 1.00 1 4 2.0E-02
12 : 0.00E+00 6.44E+01 0.000 0.0797 0.9900 0.9900 1.00 1 5 1.6E-03
13 : 0.00E+00 4.64E-01 0.000 0.0072 0.9990 0.9990 1.00 2 3 1.2E-05
14 : 0.00E+00 1.29E-02 0.000 0.0277 0.9900 0.9900 1.00 5 30 3.5E-07
15 : 0.00E+00 3.86E-03 0.125 0.2995 0.9000 0.9000 0.98 7 1 1.1E-07
16 : 0.00E+00 1.80E-03 0.000 0.4675 0.9000 0.9000 0.94 4 4 5.0E-08
17 : 0.00E+00 3.81E-04 0.000 0.2115 0.9000 0.9000 0.86 4 9 1.2E-08
18 : 0.00E+00 7.79E-05 0.000 0.2044 0.9000 0.9000 0.49 10 7 4.3E-09
19 : 0.00E+00 6.79E-05 0.000 0.8719 0.9000 0.9000 -0.24 8 9 4.2E-09
Run into numerical problems.
iter seconds digits c*x b*y
19 1.5 Inf 0.0000000000e+00 0.0000000000e+00
|Ax-b| = 2.3e-09, [Ay-c]_+ = 1.8E-15, |x|= 5.9e+00, |y|= 1.3e+00
Detailed timing (sec)
Pre IPM Post
1.450E-01 9.040E-01 3.200E-02
Max-norms: ||b||=0, ||c|| = 0,
Cholesky |add|=0, |skip| = 5, ||L.L|| = 15770.4.
Hmm, something went wrong!
ans =
'Numerical problems (SeDuMi-1.3)'
ans =
'Numerical problems '
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Thanks for advising me on finding the answer
Johan Löfberg
Mar 7, 2019, 11:52:32 AM3/7/19
to YALMIP
First, transpose in matlab is simply '
Second, your data is nasty (10^5 etc), so I wouldn't have too much hope, in particular with sedumi. Try mosek
Third, your model is ill-posed as 0 is a feasible solution. Pb>= eye(n) would be a start to dehomogenize the problem
mohammad hassan
Mar 7, 2019, 5:16:23 PM3/7/19
to YALMIP
Thanks alot
I was able to get a fairly good answer by setting the parameters.
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