The viscosity subdifferential of the rank function via the corresponding subdifferential of its Moreau envelopes

Jean-Baptiste Hiriart-Urruty (1) , Hai Yen Le (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 VAST - Vietnam Academy of Science and Technology

We derive the so-called viscosity subdifferential of the rank function via a limiting process applied to the Moreau envelopes of the rank function. Before that, we obtain the explicit expressions of all the generalized subdifferentials of the Moreau envelopes of the rank function.

Mots clés: Rank function; Singular values of a matrix; Moreau envelopes; Generalized subdifferentials; Viscosity subdifferential

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Jean-Baptiste Hiriart-Urruty, Hai Yen Le. The viscosity subdifferential of the rank function via the corresponding subdifferential of its Moreau envelopes. Acta Mathematica Vietnamica, 2015, 40 (4), pp.735-746. ⟨10.1007/s40306⟩. ⟨hal-01975637⟩