Journal of Convex Analysis 33 (2026), No. 1&2, 267--291
Copyright Heldermann Verlag 2026
Variational Analysis of Orthogonally Invariant Norm Cones of Symmetric Matrices
Yule Zhang
School of Science, Dalian Maritime University, Dalian, China
ylzhang@dlmu.edu.cn
Jihong Zhang
School of Science, Shenyang Ligong University, Shenyang, China
zjh7815040x@163.com
Liwei Zhang
(1) National Frontiers Science Center, Industrial Intelligence & Systems Optimization, Northeastern University, Shenyang, China
(2) Key Laboratory of Data Analytics, Northeastern University, Ministry of Education, Shenyang, China
zhanglw@mail.neu.edu.cn
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.
Keywords: Orthogonally invariant norm cone, variational analysis, tangent cone, normal cone, outer second-order tangent set, projection, directional derivative, B-subdifferential.
MSC: 90C30.
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