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

Robert Baier; Elza Farkhi; Vera Roshchina

doi:10.1007/s10957-013-0401-x

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

Robert Baier, Elza Farkhi, Vera Roshchina

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	391-414
Number of pages	24
Journal	Journal of Optimization Theory and Applications
Volume	160
Issue number	2
DOIs	https://doi.org/10.1007/s10957-013-0401-x
State	Published - Feb 2014

Keywords

Difference of convex (delta-convex, DC) functions
Differences of sets
Directional derivatives
Nonconvex subdifferentials

All Science Journal Classification (ASJC) codes

Control and Optimization
Applied Mathematics
Management Science and Operations Research

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10.1007/s10957-013-0401-x

Cite this

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title = "Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure",

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 = "Difference of convex (delta-convex, DC) functions, Differences of sets, Directional derivatives, Nonconvex subdifferentials",

author = "Robert Baier and Elza Farkhi and Vera Roshchina",

note = "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 {\textquoteleft}Self-sustaining Regions Research and Innovation Initiative{\textquoteright}, an Australian Government Collaborative Research Network (CRN).",

year = "2014",

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doi = "10.1007/s10957-013-0401-x",

language = "الإنجليزيّة",

volume = "160",

pages = "391--414",

journal = "Journal of Optimization Theory and Applications",

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number = "2",

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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

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U2 - 10.1007/s10957-013-0401-x

DO - 10.1007/s10957-013-0401-x

M3 - مقالة

SN - 0022-3239

VL - 160

SP - 391

EP - 414

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 2

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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