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

Youyicun Lin () and Shenglong Hu ()
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Youyicun Lin: Hangzhou Dianzi University
Shenglong Hu: Hangzhou Dianzi University

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 2, No 12, 702-724

Abstract: 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.

Keywords: Spectraplex; Generalized matrix simplex; Projection; $${\text {B}}$$ B -subdifferential; Han-Sun Jacobian; 15A18; 15A69; 26E25; 58C20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-021-01988-8

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