B-Subdifferential of the Projection onto the Generalized Spectraplex

In this paper, a complete characterization of the 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 B -subdifferential as well as the Han-Sun J...

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Veröffentlicht in:	Journal of optimization theory and applications 2022-02, Vol.192 (2), p.702-724
Hauptverfasser:	Lin, Youyicun, Hu, Shenglong
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Applications of Mathematics Calculus of Variations and Optimal Control Optimization Engineering Mapping Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Projection Projectors Theory of Computation
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Beschreibung
Zusammenfassung:	In this paper, a complete characterization of the 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 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.
ISSN:	0022-3239 1573-2878
DOI:	10.1007/s10957-021-01988-8