TY - JOUR
T1 - Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure
AU - Baier, Robert
AU - Farkhi, Elza
AU - Roshchina, Vera
N1 - Funding Information:
Acknowledgements The research is partially supported by The Hermann Minkowski Center for Geometry at Tel Aviv University, Tel Aviv, Israel and by the University of Ballarat ‘Self-sustaining Regions Research and Innovation Initiative’, an Australian Government Collaborative Research Network (CRN).
PY - 2014/2
Y1 - 2014/2
N2 - 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.
AB - 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.
KW - Difference of convex (delta-convex, DC) functions
KW - Differences of sets
KW - Directional derivatives
KW - Nonconvex subdifferentials
UR - http://www.scopus.com/inward/record.url?scp=84896489593&partnerID=8YFLogxK
U2 - 10.1007/s10957-013-0401-x
DO - 10.1007/s10957-013-0401-x
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AN - SCOPUS:84896489593
VL - 160
SP - 391
EP - 414
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
SN - 0022-3239
IS - 2
ER -