On the Generalized Jacobian of the Inverse of a Lipschitzian Mapping

Marián Fabian (1) , Jean-Baptiste Hiriart-Urruty (2) , Edouard Pauwels (3)

1 CAS - Czech Academy of Sciences [Prague]
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage

The objective of this short note is to provide an estimate of the generalized Jacobian of the inverse of a Lipschitzian mapping when Clarke’s inverse function theorem applies. Contrary to the classical C1 case, inverting matrices of the generalized Jacobian is not enough. Simple counterexamples show that our results are sharp.

Mots clés: Inverse function theorem; Lipschitzian mapping; Generalized jacobian

Domaines: Optimisation et contrôle [math.OC]

Marián Fabian, Jean-Baptiste Hiriart-Urruty, Edouard Pauwels. On the Generalized Jacobian of the Inverse of a Lipschitzian Mapping. Set-Valued and Variational Analysis, 2022, ⟨10.1007/s11228-022-00640-5⟩. ⟨hal-03673260⟩