Computing or bounding a modified Ky Fan norm

[Nathaniel_Johnston]

For completeness’ sake, this question can be solved by using Madeleine Udell’s wonderful answer here elsewhere on these forums:

Represent Schatten-p norm in CVX

Actually, any symmetric monotone function of the singular values of a matrix is DCP-representable. See Ben-Tal and Nemirovski “Lectures on Modern Convex Optimization”, Proposition 4.2.2. But the best representation (presented there, at least) is huge! Let’s see how this works for a PSD matrix A. (The case of rectangular matrices is similar.) the sum S_k(A) of the top k eigenvalues of A is the solution to the problem minimize sk + Tr(Z) subject to Z ⪰ 0 A ⪰ 0 Z + sI ⪰ A …