The directed and Rubinov subdifferentials of quasidifferentiable functions, Part II: Calculus - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Nonlinear Analysis: Theory, Methods and Applications Année : 2012

The directed and Rubinov subdifferentials of quasidifferentiable functions, Part II: Calculus

Résumé

We continue the study of the directed subdifferential for quasidifferentiable functions started in [R. Baier, E. Farkhi, V. Roshchina, The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I: Definition and examples (this journal)]. Calculus rules for the directed subdifferentials of sum, product, quotient, maximum and minimum of quasidifferentiable functions are derived. The relation between the Rubinov subdifferential and the subdifferentials of Clarke, Dini, Michel-Penot, and Mordukhovich is discussed. Important properties implying the claims of Ioffe's axioms as well as necessary and sufficient optimality conditions for the directed subdifferential are obtained.

Dates et versions

hal-00724863 , version 1 (22-08-2012)

Identifiants

Citer

Robert Baier, Elza Farkhi, Vera Roshchina. The directed and Rubinov subdifferentials of quasidifferentiable functions, Part II: Calculus. Nonlinear Analysis: Theory, Methods and Applications, 2012, 75 (3), pp.1058-1073. ⟨10.1016/j.na.2011.04.073⟩. ⟨hal-00724863⟩
81 Consultations
1 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More