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$${\text {B}}$$ B -Subdifferential of the Projection onto the Generalized Spectraplex

Author

Listed:
  • Youyicun Lin

    (Hangzhou Dianzi University)

  • Shenglong Hu

    (Hangzhou Dianzi University)

Abstract

In this paper, a complete characterization of the $${\text {B}}$$ B -subdifferential with explicit formula for the projection mapping onto the generalized spectraplex (aka generalized matrix simplex) is derived. The derivation is based on complete characterizations of the $${\text {B}}$$ B -subdifferential as well as the Han-Sun Jacobian of the projection mapping onto the generalized simplex. The formula provides tools for further computations and nonsmooth analysis involving this projection.

Suggested Citation

  • Youyicun Lin & Shenglong Hu, 2022. "$${\text {B}}$$ B -Subdifferential of the Projection onto the Generalized Spectraplex," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 702-724, February.
    • Handle: RePEc:spr:joptap:v:192:y:2022:i:2:d:10.1007_s10957-021-01988-8
    DOI: 10.1007/s10957-021-01988-8
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    References listed on IDEAS

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    1. Defeng Sun & Jie Sun, 2002. "Semismooth Matrix-Valued Functions," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 150-169, February.
    2. J. Han & D. Sun, 1997. "Newton and Quasi-Newton Methods for Normal Maps with Polyhedral Sets," Journal of Optimization Theory and Applications, Springer, vol. 94(3), pages 659-676, September.
    3. Jong-Shi Pang & Defeng Sun & Jie Sun, 2003. "Semismooth Homeomorphisms and Strong Stability of Semidefinite and Lorentz Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 39-63, February.
    4. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
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