@Erling is correct. That result is one of my favorites in all of math, right up there iwith Jensen’s inequality.
There is howeverr a dumb way to do this in CVX, which is not dumb when you don’t want the sum of all the eigenvalues.
lambda_sum_largest Sum of the k largest eigenvalues of a symmetric matrix.
For square matrix X, lambda_sum_largest(X,K) is SUM_LARGEST(EIG(X),k)
if X is Hermitian or symmetric and real; and +Inf otherwise.
An error results if X is not a square matrix.
Disciplined convex programming information:
lambda_sum_largest is convex and nonmonotonic (at least with
respect to elementwise comparison), so its argument must be affine.