In CVX, I encounter a problem. I want to multiply a Matrix of 2x4 with its transpose. I know the result must be positive definite. However, it couldn't let me do the multiplication directly. Says: Disciplined convex programming error:Only scalar quadratic forms can be specified in CVX. What can I do?

cvx_begin variable power_allocation(length(anchor_coordinate.x),1) minimize sum(power_allocation) subject to Matrix = process_matrix_inv'*(observation_matrix(:,:,t*n+1)'*diag(power_allocation.*path_loss(:,t*n+1))* observation_matrix(:,:,t*n+1)+prior_infor(:,:,t*n))*process_matrix_inv; A = Matrix(1:2,3:6)*D*Matrix(1:2,3:6)'; trace_inv(Matrix(1:2,1:2)-A) <= MSE_limit; power_allocation <= power_max; power_allocation >= power_min; cvx_end

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    $\begingroup$ the matrix D is a symmetrical matrix. $\endgroup$
    – tian qing
    Mar 12 '16 at 11:05
  • $\begingroup$ I tone the end of the post down a bit. $\endgroup$
    – Dirk
    Mar 12 '16 at 17:12
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    $\begingroup$ As a small remark, the product of a matrix and its transpose doesn't have to be positive definite. It can be positive semidefinite. Try, for example, with a matrix that has a zero column, or is in fact entirely composed of zeros. $\endgroup$ Mar 12 '16 at 17:54

In CVX, you can use


to implement

$ (Ax-b)^{T}Q(Ax-b) $

See the section of the manual on scalar quadratic forms.

  • $\begingroup$ Dear professor, thank you for your reply. However, in my case, the (A*x-b) part is a tensor with 2*4 scale. And in CVX, it only permits me to input a vector. How could I fix that ? $\endgroup$
    – tian qing
    Mar 14 '16 at 11:17
  • $\begingroup$ And all I want is to represent the sum of first two elements in the trace line of an inverse of Matrix. $\endgroup$
    – tian qing
    Mar 14 '16 at 11:23

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