Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Orthogonally invariant norm cone
  • variational analysis
  • tangent cone
  • normal cone
  • outer second-order tangent set
  • projection
  • directional derivative
  • B-subdifferential

Mathematics Subject Classification

90C30

Suggested citation

Y. Zhang, J. Zhang, L. Zhang. “Variational Analysis of Orthogonally Invariant Norm Cones of Symmetric Matrices.” Journal of Convex Analysis 33 (2026), No. 1&2, 267–291. https://doi.org/10.68381/jca33017

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press.