How to use CVX minimize “trace(inv(X))”, where X is an N*N matrix

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How to use CVX minimize “trace(inv(X))”, where X is an N*N matrix

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help trace_inv

trace_inv Trace of the inverse of a PSD matrix.
For square matrix X, trace_inv(X) is TRACE(INV(X)) if X is Hermitian
or symmetric and positive definite; and +Inf otherwise.

  An error results if X is not a square matrix.

  Disciplined convex programming information:
      trace_inv is convex and nonmonotonic (at least with respect to
      elementwise comparison), so its argument must be affine.

This is listed in http://cvxr.com/cvx/doc/funcref.html#new-functions . You should read the entire CVX Users’ Guide.