First order sensitivity analysis of symplectic eigenvalues
Linear Algebra and Its Applications
For every 2n×2n positive definite matrix A there are n positive numbers d1(A)≤…≤dn(A) associated with A called the symplectic eigenvalues of A. It is known that dm are continuous functions of A but are not differentiable in general. In this paper, we show that the directional derivative of dm exists and derive its expression. We also discuss various subdifferential properties of dm such as Clarke and Michel-Penot subdifferentials.
Mishra, Hemant Kumar, "First order sensitivity analysis of symplectic eigenvalues" (2020). Journal Articles. 89.