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

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Abstract

In this paper, a complete characterization of the \({\text {B}}\)-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 \({\text {B}}\)-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.

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Notes

  1. The general case is derived by a similar proof through replacing suitably p by \(p'\) and w by \(w'\) as (21).

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Acknowledgements

The authors are grateful to the editors and the anonymous referees’ for their valuable comments. This work is partially supported by National Science Foundation of China (Grant Nos. 11771328,11801502 and 12171128) and the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LD19A010002 and LY22A010022).

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Correspondence to Shenglong Hu.

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Communicated by Russell Luke.

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Lin, Y., Hu, S. \({\text {B}}\)-Subdifferential of the Projection onto the Generalized Spectraplex. J Optim Theory Appl 192, 702–724 (2022). https://doi.org/10.1007/s10957-021-01988-8

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