The Ky Fan k-norm of a matrix X \in M_n is defined as follows:

\|X\|_k := \sum_{i=1}^k \sigma_i^\downarrow(X)

(i.e., the sum of the k largest singular values of X). In CVX, there is a simple way to optimize over the set of matrices with bounded Ky Fan k-norm. For example, if we wanted to optimize over the set of matrices with Ky Fan k-norm no larger than 1, we could set one of the constraints in CVX as follows: