- Title
- The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I: Definition and examples
- Creator
- Baier, Robert; Farkhi, Elza; Roschina, Vera
- Date
- 2012
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/73762
- Identifier
- vital:7105
- Identifier
-
https://doi.org/10.1016/j.na.2011.04.074
- Identifier
- ISSN:0362-546X
- Abstract
- We extend the definition of the directed subdifferential, originally introduced in [R. Baier, E. Farkhi, The directed subdifferential of DC functions, in: A. Leizarowitz, B.S. Mordukhovich, I. Shafrir, A.J. Zaslavski (Eds.), Nonlinear Analysis and Optimization II: Optimization. A Conference in Celebration of Alex Ioffe’s 70th and Simeon Reich’s 60th Birthdays, June 18–24, 2008, Haifa, Israel, in: AMS Contemp. Math., vol. 513, AMS, Bar-Ilan University, 2010, pp. 27–43], for differences of convex functions (DC) to the wider class of quasidifferentiable functions. Such generalization efficiently captures differential properties of a wide class of functions including amenable and lower/upper-View the MathML source functions. While preserving the most important properties of the quasidifferential, such as exact calculus rules, the directed subdifferential lacks the major drawbacks of quasidifferential: non-uniqueness and “inflation in size” of the two convex sets representing the quasidifferential after applying calculus rules. The Rubinov subdifferential is defined as the visualization of the directed subdifferential.
- Relation
- Nonlinear Analysis: Theory, Methods Applications Vol. 75, no. 3 (2012), p. 1074-1088
- Rights
- Copyright Elsevier
- Rights
- Open access
- Rights
- This metadata is freely available under a CCO license
- Subject
- Subdifferentials; Quasidifferentiable functions; Differences of sets; Directed sets; Directed subdifferential; 0101 Pure Mathematics; 0102 Applied Mathematics
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