Variational Analysis of Orthogonally Invariant Norm Cones of Symmetric Matrices

This paper is devoted to the study of variational analysis of the orthogonally invariant norm cone of symmetric matrices. For a general orthogonally invariant norm cone of symmetric matrices, formulas for the tangent cone, normal cone and second-order tangent set are established. The differentiability properties of the projection operator onto the orthogonally invariant norm cone are developed, including formulas for the directional derivative and the B-subdifferential. In particular, the directional derivative is characterized by the second-order derivative of the corresponding symmetric norm, which is convenient for computation.