The Ky Fan k-norm of a matrix X \in M_n is defined as follows:
(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:
lambda_sum_largest([zeros(n),X;X',zeros(n)],k) <= 1;
My question is whether or not there is a similarly simple way to implement the following norm in CVX:
That is, I am interested in the 2-norm of the k largest singular values instead of the 1-norm of the k largest singular values.