TY - JOUR
T1 - From Quasidifferentiable to Directed Subdifferentiable Functions
T2 - Exact Calculus Rules
AU - Baier, Robert
AU - Farkhi, Elza
AU - Roshchina, Vera
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2016/11/1
Y1 - 2016/11/1
N2 - We derive exact calculus rules for the directed subdifferential defined for the class of directed subdifferentiable functions. We also state optimality conditions, a chain rule and a mean-value theorem. Thus, we extend the theory of the directed subdifferential from quasidifferentiable to directed subdifferentiable functions.
AB - We derive exact calculus rules for the directed subdifferential defined for the class of directed subdifferentiable functions. We also state optimality conditions, a chain rule and a mean-value theorem. Thus, we extend the theory of the directed subdifferential from quasidifferentiable to directed subdifferentiable functions.
KW - Difference of convex (DC) functions
KW - Directional derivatives
KW - Mean-value theorem and chain rule for nonsmooth functions
KW - Nonconvex subdifferentials
UR - http://www.scopus.com/inward/record.url?scp=84963647265&partnerID=8YFLogxK
U2 - 10.1007/s10957-016-0926-x
DO - 10.1007/s10957-016-0926-x
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AN - SCOPUS:84963647265
VL - 171
SP - 384
EP - 401
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
SN - 0022-3239
IS - 2
ER -