Two equivalent codes getting different answer

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khushi 2017-7-14

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/348790-two-equivalent-codes-getting-different-answer

编辑： Walter Roberson 2017-7-16

Code 1:

AD=[1 8 4;5 6 3;2 7 6];
dd=[1 6 7;3 6 8;2 6 5];
cvx_begin 
variables QM(3,3) 
maximize log_det(eye(3)+dd*QM)
subject to 
norm(QM*AD,'fro')<=10;
cvx_end

Code 2:

AD=[1 8 4;5 6 3;2 7 6];
dd=[1 6 7;3 6 8;2 6 5];
[RU,RS,RV]=svd(inv(AD)*dd);
cvx_begin 
variables QM(3,3) 
maximize log_det(eye(3)+RS*QM)
subject to 
norm(QM,'fro')<=10;
cvx_end

Code 2 is obtained from Code 1 by change of variables so I believe that these two codes are equivalent. However, I am getting different answers i.e. the maximum value of objective function. Is there something wrong with the change of variables?

Following are the change in variables

det(I+dd QM)=det(AD〖AD〗^(-1)+dd QM AD AD^(-1) )
=det(AD(I+AD^(-1)  dd QM AD)AD^(-1))
det(I+dd QM)=det(I+AD^(-1)  dd QM AD)=det(I+UΣV^T QM AD)=det(I+ΣV^T QM AD U)=det(I+ΣR)
norm(QM AD)=norm(VV^T QM AD U U^T )=norm(V R U^T )=trace(V R U^T U R^T V^T )=trace(R R^T)