1
$\begingroup$

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

$\endgroup$
  • 1
    $\begingroup$ 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
  • 2
    $\begingroup$ 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. $\endgroup$ – Wolfgang Bangerth Mar 12 '16 at 17:54
4
$\begingroup$

In CVX, you can use

quad_form(A*x-b,Q)

to implement

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

See the section of the manual on scalar quadratic forms.

$\endgroup$
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.