From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules

Robert Baier; Elza Farkhi; Vera Roshchina

doi:https://doi.org/10.1007/s10957-016-0926-x

From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules

Robert Baier, Elza Farkhi, Vera Roshchina

School of Mathematical Sciences

Tel Aviv University

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

Abstract

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.

Original language	English
Pages (from-to)	384-401
Number of pages	18
Journal	Journal of Optimization Theory and Applications
Volume	171
Issue number	2
DOIs	https://doi.org/10.1007/s10957-016-0926-x
State	Published - 1 Nov 2016

Keywords

Difference of convex (DC) functions
Directional derivatives
Mean-value theorem and chain rule for nonsmooth functions
Nonconvex subdifferentials

All Science Journal Classification (ASJC) codes

Management Science and Operations Research
Control and Optimization
Applied Mathematics

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Cite this

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title = "From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules",

abstract = "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.",

keywords = "Difference of convex (DC) functions, Directional derivatives, Mean-value theorem and chain rule for nonsmooth functions, Nonconvex subdifferentials",

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

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AU - Roshchina, Vera

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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

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SP - 384

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JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 2

ER -

From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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