Can cvx solve this problem?

Everything in the objective function other than p is input data.
y and a is 10 * 1 vector.
A is 10 * 1800 array.

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help matrix_frac

 matrix_frac   Matrix fractional function.
      matrix_frac(x,Y), where Y is a square matrix and x is a vector of the
      same size, computes x'*(inv(Y)*x) if Y is Hermitian positive definite, and
      +Inf otherwise.
      An error results if Y is not a square matrix, or the size of
      the vector x does not match the size of matrix Y.
      Disciplined convex programming information:
          matrix_frac is convex and nonmonotonic (at least with respect to
          elementwise comparison), so its argument must be affine.