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Journal Articles Nonlinear Analysis: Theory, Methods and Applications Year : 2012

The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I: Definition and examples

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- 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.

Dates and versions

hal-00724862 , version 1 (22-08-2012)

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Cite

Robert Baier, Elza Farkhi, Vera Roshchina. The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I: Definition and examples. Nonlinear Analysis: Theory, Methods and Applications, 2012, 75 (3), pp.1074-1088. ⟨10.1016/j.na.2011.04.074⟩. ⟨hal-00724862⟩
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