For convex orthogonally invariant matrix functions, the paper derives explicit second subderivatives and sufficient conditions for twice epi-differentiability, including a closed-form second-order epi-derivative for the nuclear norm.
and Toh, K.C.: An Introduction to a Class of Matrix Cone Programming
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Twice Epi-Differentiability of Orthogonally Invariant Matrix Functions and Application
For convex orthogonally invariant matrix functions, the paper derives explicit second subderivatives and sufficient conditions for twice epi-differentiability, including a closed-form second-order epi-derivative for the nuclear norm.