Geodesic
Variational Analysis of Spectral Functions Simplified
Journal of convex analysis, Tome 25 (2018) no. 1, pp. 119-134
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Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their subdifferentials to the subdifferentials of their diagonal restrictions. This paper presents a new, short, and revealing derivation of this result. The argument has a direct analogue for spectral functions of Hermitian matrices, and for singular value functions of rectangular matrices.
Classification : 14A18, 49J52, 46G05, 26B05, 49J53
Mots-clés : Eigenvalues, singular values, nonsmooth analysis, proximal mapping, subdifferential, Hessian, quadratic growth, group actions 
@article{JCA_2018_25_1_JCA_2018_25_1_a7,
     author = {D. Drusvyatskiy and C. Paquette},
     title = {Variational {Analysis} of {Spectral} {Functions} {Simplified}},
     journal = {Journal of convex analysis},
     pages = {119--134},
     year = {2018},
     volume = {25},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_1_JCA_2018_25_1_a7/}
}
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D. Drusvyatskiy; C. Paquette. Variational Analysis of Spectral Functions Simplified. Journal of convex analysis, Tome 25 (2018) no. 1, pp. 119-134. http://geodesic.mathdoc.fr/item/JCA_2018_25_1_JCA_2018_25_1_a7/