Ask for help if you have a semi-determined planning problem

1

Here’s my program, and the error message is as follows:
Warning: A non-empty cvx problem already exists in this scope.
It is being overwritten.

Position: CVXPROB (line 28)
Location: cvx_begin (line 41)
Location: untitled (row 4)

Successive approximation method to be employed.
SDPT3 will be called several times to refine the solution.
Original size: 1267 variables, 494 equality constraints
1 exponentials add 8 variables, 5 equality constraints

Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------±--------------------------------±--------
You can’t use a value of type struct as an index.

Error cvxprob/solve (line 253)
[ x, status, tprec, iters2, y, z ] = shim.solve( [ At, Anew2 ], [ b ; bnew ], c, cones, true, prec, solv.settings, eargs{:} );

Error cvx_end (line 88)
solve( prob );

Error untitled (line 58)
cvx_end
Please point out how this should be corrected, and I would be very grateful！

clc;clear;close
H=[0.25 0;0 0.25]; G=[1;0];D=[10 0; 0 10];P=[10 10;10 0;1 11];
cvx_begin sdp
variable N(1,2);
variable W(2,2) symmetric ;

 variable r11(1,1) nonnegative;variable r12(1,1) nonnegative;variable r13(1,1) nonnegative;variable r14(1,1) nonnegative;variable r15(1,1) nonnegative;variable r16(1,1) nonnegative;
 variable r21(1,1) nonnegative;variable r22(1,1) nonnegative;variable r23(1,1) nonnegative;variable r24(1,1) nonnegative;variable r25(1,1) nonnegative;variable r26(1,1) nonnegative;
 variable r31(1,1) nonnegative;variable r32(1,1) nonnegative;variable r33(1,1) nonnegative;variable r34(1,1) nonnegative;variable r35(1,1) nonnegative;variable r36(1,1) nonnegative
 
 variable a11(40,40) semidefinite diagonal;variable a12(40,40) semidefinite diagonal;variable a13(40,40) semidefinite diagonal;variable a14(40,40) semidefinite diagonal;variable a15(40,40) semidefinite diagonal;variable a16(40,40) semidefinite diagonal;
 variable a21(40,40) semidefinite diagonal;variable a22(40,40) semidefinite diagonal;variable a23(40,40) semidefinite diagonal;variable a24(40,40) semidefinite diagonal;variable a25(40,40) semidefinite diagonal;variable a26(40,40) semidefinite diagonal;
 variable a31(40,40) semidefinite diagonal;variable a32(40,40) semidefinite diagonal;variable a33(40,40) semidefinite diagonal;variable a34(40,40) semidefinite diagonal;variable a35(40,40) semidefinite diagonal;variable a36(40,40) semidefinite diagonal;

 variable b11(2,2) semidefinite diagonal;variable b12(2,2) semidefinite diagonal;variable b13(2,2) semidefinite diagonal;variable b14(2,2) semidefinite diagonal;variable b15(2,2) semidefinite diagonal;variable b16(2,2) semidefinite diagonal;
 variable b21(2,2) semidefinite diagonal;variable b22(2,2) semidefinite diagonal;variable b23(2,2) semidefinite diagonal;variable b24(2,2) semidefinite diagonal;variable b25(2,2) semidefinite diagonal;variable b26(2,2) semidefinite diagonal;
 variable b31(2,2) semidefinite diagonal;variable b32(2,2) semidefinite diagonal;variable b33(2,2) semidefinite diagonal;variable b34(2,2) semidefinite diagonal;variable b35(2,2) semidefinite diagonal;variable b36(2,2) semidefinite diagonal;

%
%maximize (log_det(W))
%maximize log_det(W)
minimize -log_det(W)
subject to
HW[0.0100;0.0900]>=-ones(2,1);HW[0.0100;0.0900]<=ones(2,1);
HW[-0.1000;0.1000]>=-ones(2,1);HW[0.1000;-0.0000]<=ones(2,1);
HW[0.0100;0.0900]<=ones(2,1);HW[-0.1000;0.1000]<=ones(2,1);
GN[-0.1000;0.1000]>=-ones(2,1);GN[0.0100;0.0900]>=-ones(2,1);
GN[-0.1000;0.1000]>=-ones(2,1);GN[-0.1000;0.1000]<=ones(2,1);
GN[0.0100;0.0900]<=ones(2,1);GN[-0.1000;0.1000]<=ones(2,1);
X1=[-1.1149 0.7390 4.4272 7.0072 6.9355 3.8999 2.2305 1.3877 -0.8361 -3.0095 -6.4296 -7.5664 -8.5995 -9.7856 -9.2884 -10.1804 -10.5304 -11.9561 -13.1271 -14.0937;
1.3482 1.7756 2.4331 0.8166 0.3907 -0.9379 -0.1125 0.1498 -2.0075 -2.9587 -1.2236 -0.0307 -1.4458 -1.1847 -0.5079 0.1705 0.5498 -0.6186 -1.2793 0.2288];
X2=[-1.1149 0.7390 4.4272 7.0072 6.9355 3.8999 2.2305 1.3877 -0.8361 -3.0095 -6.4296 -7.5664 -8.5995 -9.7856 -9.2884 -10.1804 -10.5304 -11.9561 -13.1271 -14.0937 -14.1846;
1.3482 1.7756 2.4331 0.8166 0.3907 -0.9379 -0.1125 0.1498 -2.0075 -2.9587 -1.2236 -0.0307 -1.4458 -1.1847 -0.5079 0.1705 0.5498 -0.6186 -1.2793 0.2288 -0.7305];
U=[-0.6334 1.7316 -0.4373 -0.9071 -1.3922 -0.4116 -0.5011 -1.4755 -0.2598 -1.6339 0.4585 -1.9561 0.2930 1.1589 -1.0585 -0.2079 0.2774 -1.7544 -0.0148 0.5693];
e1=[1;0;0];e2=[0;1;0];e3=[0;0;1];
d=[D*[0.7390;1.7756];D*[4.4272;2.4331];D*[7.0072;0.8166];D*[6.9355;0.3907];D*[3.8999;0.9379];D*[2.2305; -0.1125];D*[1.3877;0.1498];D*[-0.8361;-2.0075];D*[-3.0095;-2.9587];D*[-6.4296;-1.2236];D*[-7.5664;
-0.0307];D*[-8.5995;-1.4458];D*[-9.7856;-1.1847];D*[-9.2884;-0.5079];D*[-10.1804;0.1705];D*[-10.5304;0.5498];D*[-11.9561;-0.6186];D*[-13.1271;-1.2793];D*[-14.0937;0.2288];D*[-14.1846;-0.7305]];
z=kron([X1;U]‘,D);
g11=([W;N][-0.1000;0.1000])';
g1=kron(g11,eye(2));
g22=([W;N][0.1000;-0.0000])’;
g2=kron(g22,eye(2));
g33=([W;N][0.0100;0.0900])';
g3=kron(g33,eye(2));
g44=([W;N][0.1000;-0.1000])‘;
g4=kron(g44,eye(2));
g55=([W;N][-0.1000;0.0000])';
g5=kron(g55,eye(2));
g66=([W;N][-0.0100;-0.0900])’;
g6=kron(g66,eye(2));
[r11-ones(40,1)‘a11ones(40,1)-[1;1]‘b11[1;1]+d’a11d,-d’a11z,zeros(1,2),zeros(1,2);-z’a11d,z’a11z,zeros(6,2),g1’;zeros(2,1),zeros(2,6),D’b11D,eye(2);zeros(2,1),g1,eye(2),W+W’-r11*P’e1e1’P] == semidefinite(11);
[r11-ones(40,1)‘a11ones(40,1)-[1;1]‘b11[1;1]+d’a11d,-d’a11z,zeros(1,2),zeros(1,2);-z’a11d,z’a11z,zeros(6,2),g1’;zeros(2,1),zeros(2,6),D’b11D,eye(2);zeros(2,1),g1,eye(2),W+W’-r11P’e1e1’P] == semidefinite(11);
[r12-ones(40,1)‘a12ones(40,1)-[1;1]‘b12[1;1]+d’a12d,-d’a12z,zeros(1,2),zeros(1,2);-z’a12d,z’a12z,zeros(6,2),g1’;zeros(2,1),zeros(2,6),D’b12D,eye(2);zeros(2,1),g1,eye(2),W+W’-r12P’e1e1’P] == semidefinite(11);
[r13-ones(40,1)‘a13ones(40,1)-[1;1]‘b13[1;1]+d’a13d,-d’a13z,zeros(1,2),zeros(1,2);-z’a13d,z’a13z,zeros(6,2),g1’;zeros(2,1),zeros(2,6),D’b13D,eye(2);zeros(2,1),g1,eye(2),W+W’-r13P’e1e1’P] == semidefinite(11);
[r14-ones(40,1)‘a14ones(40,1)-[1;1]‘b14[1;1]+d’a14d,-d’a14z,zeros(1,2),zeros(1,2);-z’a14d,z’a14z,zeros(6,2),g1’;zeros(2,1),zeros(2,6),D’b14D,eye(2);zeros(2,1),g1,eye(2),W+W’-r14P’e1e1’P] == semidefinite(11);
[r15-ones(40,1)‘a15ones(40,1)-[1;1]‘b15[1;1]+d’a15d,-d’a15z,zeros(1,2),zeros(1,2);-z’a15d,z’a15z,zeros(6,2),g1’;zeros(2,1),zeros(2,6),D’b15D,eye(2);zeros(2,1),g1,eye(2),W+W’-r15P’e1e1’P] == semidefinite(11);
[r16-ones(40,1)‘a16ones(40,1)-[1;1]‘b16[1;1]+d’a16d,-d’a16z,zeros(1,2),zeros(1,2);-z’a16d,z’a16z,zeros(6,2),g1’;zeros(2,1),zeros(2,6),D’b16D,eye(2);zeros(2,1),g1,eye(2),W+W’-r16P’e1e1’*P] == semidefinite(11);
cvx_end
cvx_optval

2

Make sure you are using CVX 2.2.2 or CVX 2.2. Do not use CVX 3.0beta, which is riddled with bugs. It’s possible your MATLAB session was corrupted.

In any event, if you have Mosek available as solver, use it.

Otherwise, follow the instructions at CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions .

3

Mark, I have a question that I have to ask you, I choose different data X1 and U for the above code, and the result of the matrix W is the same or only 0.01 difference, what is the reason for this?

4

You haven’;t provided enough information to support a meaningful answer.