- Title
- The directed and Rubinov subdifferentials of quasidifferentiable functions, Part II: Calculus
- Creator
- Baier, Robert; Farkhi, Elza; Roschina, Vera
- Date
- 2012
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/73739
- Identifier
- vital:7106
- Identifier
-
https://doi.org/10.1016/j.na.2011.04.073
- Identifier
- ISSN:0362-546X
- Abstract
- 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.
- Relation
- Nonlinear Analysis: Theory, Methods & Applications Vol. 75, no. 3 (2012), p. 1058-1073
- Rights
- Copyright Elsevier
- Rights
- This metadata is freely available under a CCO license
- Subject
- Subdifferentials; Quasidifferentiable functions; Differences of sets; Directed sets; Directed subdifferential; Rubinov subdifferential; 0101 Pure Mathematics; 0102 Applied Mathematics
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