Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure

Robert Baier (), Elza Farkhi () and Vera Roshchina ()
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Robert Baier: University of Bayreuth
Elza Farkhi: Tel Aviv University
Vera Roshchina: University of Ballarat

Journal of Optimization Theory and Applications, 2014, vol. 160, issue 2, No 2, 414 pages

Abstract: 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.

Keywords: Nonconvex subdifferentials; Directional derivatives; Difference of convex (delta-convex; DC) functions; Differences of sets (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0401-x

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