Abstract

Matrix variables are ubiquitous in modern optimization, in part because variational properties of useful matrix functions often expedite standard optimization algorithms. Convexity is one important such property: permutation-invariant convex functions of the eigenvalues of a symmetric matrix are convex, leading to the wide applicability of semidefinite programming algorithms. We prove the analogous result for the property of identifiability, a notion central to many active-set-type optimization algorithms.