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2021 | OriginalPaper | Chapter

4. The Subdifferential of a Convex Function

Authors : Adina Chirilă, Marin Marin, Andreas Öchsner

Published in: Distribution Theory Applied to Differential Equations

Publisher: Springer International Publishing

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Abstract

In this chapter, the first section presents the definitions of Gateaux differentiable functions and of Frechet differentiable functions and the concept of subdifferentiability. Monotone and maximal monotone operators are defined. Minty’s theorem is proved. The subdifferential is shown to be a maximal monotone operator. The conjugate function is used to transform a minimization problem into a maximization problem and conversely. Finally, the additivity of the subdifferential is studied.

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previous chapter Convex and Lower-Semicontinuous Functions
next chapter Evolution Equations
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Metadata
Title
The Subdifferential of a Convex Function
Authors
Adina Chirilă
Marin Marin
Andreas Öchsner
Copyright Year
2021
Book
Distribution Theory Applied to Differential Equations

Print ISBN: 978-3-030-67158-7

Electronic ISBN: 978-3-030-67159-4

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-67159-4_4