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Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure |
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| Authors: | Robert Baier Elza Farkhi Vera Roshchina |
| Affiliation: | 1. Chair of Applied Mathematics, University of Bayreuth, 95440, Bayreuth, Germany 2. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel 3. Collaborative Research Network, University of Ballarat, F Building, Mount Helen Campus, PO BOX 663, Ballarat, VIC, 3353, Australia |
| Abstract: | We show that the directed subdifferential introduced for differences of convex (delta-convex, DC) functions by Baier and Farkhi can be constructed from the directional derivative without using any information on the delta-convex structure of the function. The new definition extends to a more general class of functions, which includes Lipschitz functions definable on o-minimal structure and quasidifferentiable functions. |
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