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From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules

Title data

Baier, Robert ; Farkhi, Elza ; Roshchina, Vera:
From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules.
University of Bayreuth, Germany; Tel Aviv University, Israel; RMIT, Australia
Bayreuth , 2016 . - 23 p.

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Project information

Project financing: The Hermann Minkowski Center for Geometry at Tel Aviv University, Tel Aviv, Israel

Abstract in another language

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.

Further data

Item Type: Preprint, postprint, working paper, discussion paper
Refereed: Yes
Additional notes: Contents:
1. Introduction
2. Calculus Rules
2.1 Algebraic operations
2.2 Pointwise maximum and minimum
3. Optimality Conditions
4. Chain Rule and Mean-Value Theorem
5. Conclusions

revised version (February 2016) and first version (July 2015) published in arXiv
Keywords: nonconvex subdifferentials; directional derivatives; difference of convex (DC) functions; mean-value theorem and chain rule for nonsmooth functions
Subject classification: Mathematics Subject Classification Code: 49J52 90C26 26B25 58C20
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 02 Jul 2015 07:00
Last Modified: 02 Mar 2016 06:27
URI: https://eref.uni-bayreuth.de/id/eprint/15712

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