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$${\text {B}}$$ B -subdifferentials of the projection onto the matrix simplex

Author

Listed:
  • Shenglong Hu

    (Hangzhou Dianzi University)

  • Guoyin Li

    (University of New South Wales)

Abstract

An important tool in matrix optimization problems is the strong semismoothness of the projection mapping onto the cone of real symmetric positive semidefinite matrices, and the explicit formula for its $${\text {B}}$$ B (ouligand)-subdifferentials. In this paper, we examine the corresponding results for the so-called matrix simplex, that is, the set of real symmetric positive semidefinite matrices whose traces are equal to one. This result complements the current literature and enlarges the toolbox of matrix spectral operators whose $${\text {B}}$$ B -subdifferentials are explicitly formulated. Since the matrix simplex frequently arises in subproblems for solving matrix optimization problems, the derived results can potentially serve as a useful tool for efficiently solving these problems. As an illustration, we present a numerical example to demonstrate that the proposed approach can outperform the existing approaches which used projection mapping onto positive semidefinite matrix cone directly.

Suggested Citation

  • Shenglong Hu & Guoyin Li, 2021. "$${\text {B}}$$ B -subdifferentials of the projection onto the matrix simplex," Computational Optimization and Applications, Springer, vol. 80(3), pages 915-941, December.
  • Handle: RePEc:spr:coopap:v:80:y:2021:i:3:d:10.1007_s10589-021-00316-0
    DOI: 10.1007/s10589-021-00316-0
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    References listed on IDEAS

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